straight lines dpp -11th elite
TRANSCRIPT
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Straight Lines DPP- 11th Elite
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Q1. The vertices of a triangle ABC are A(-2, 3), B(2, -1) and C(4, 0). Find cos A.
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Q2. Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
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Q3. Find the coordinates of the points which trisect the line segment joining (1, -2) and (-3, 4)
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Q4. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by the X-axis.
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Q5. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by x + y - 1 = 0
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Q6. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by 2x + y + 1 = 0.
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Q7. The coordinates of the midpoints of the sides of a triangle are (1, 1), (3, 2) and (4, 1). Find the coordinates of its vertices.
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Q8. Determine the ratio in which the line 3x + y - 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
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Q9. If the midpoints of a triangle are (2, 0), (2, 1) and (0, 1) then find coordinates of its vertices.
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Q10. Find the orthocentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4).
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Q11. If the circumcentre of an acute angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and(2a, -2a), then find the orthocentre.
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Q12. Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, then coordinates of third vertex are
(4, 7)
(-4, 7)
(-4, -7)
None of these
A
B
C
D
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Q13. Two vertices of a ΔABC are A(0, 0), B(0, 2) and C(2, 0). Find the distance between the circumcentre and orthocentre.
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Q14. Orthocentre and circumcentre of a ΔABC are (a, b) and (c, d), respectively. If the coordinates of the vertex A are (x
1, y
1), then find the coordinates of the
middle point of BC.
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Q15. If the coordinates of two points A and B are (3, 4) and (5, -2), respectively. Find the coordinates of any point P if PA = PB and area of ΔPAB = 10 sq. units.
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Q16. If ⍺, β, γ are the roots of the equation x3 - 3px2 + 3qx - 1 = 0, then find the centroid of the triangle whose vertices are (⍺, β + γ), (β, ⍺ + γ), (γ, ⍺ + β)
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Q17. Find the area of a triangle whose vertices are (t, t + 2), (t + 3, t) and (t + 2, t + 2)
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Q18. Find the area of a pentagon whose vertices are (4, 3), (-5, 6) (0, 7), (3, -6) and (-7, -2)
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Q19. Find the value of k if (k + 1, 2 - k), (1 - k, - k) and (2 + k, 3 - k) are collinear.
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Q20. Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.
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Q21. The locus of a point which moves such that its distance from the point(0, 0) is twice its distance from the y-axis, is
x2 - y2 = 0
3x2 - y2 = 0
x2 - 3y2 = 0
None of these
A
B
C
D
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Q22. Find the locus of a point whose coordinates are given by x = 2t3 + t, y = t - 1, where t is a parameter
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Q23. Find the locus of a movable point P, for which the sum of its distance from (0, 3) and (0, -3) is 8.
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Q24. If P be the mid-point of the straight line joining the points A(1, 2) and Q where Q is a variable point on the curve x2 + y2 + x + y = 0. Find the locus of P.
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Q25. Find the locus of a point such that the sum of its distance from the points (0, 2) and (0, -2) is 6.
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Q26. Find the equation of the curve 2x2 + y2 - 3x + 5y - 8 = 0, when the origin is shifted to the point (-1, 2) without changing the direction of the axes.
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Q27. The equation of a curve referred to the new axes retaining their directions and origin is (4, 5) is x2 + y2 = 36. Find the equation referred to the original axes.
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Q28. Find the equation to which the equation x2 + 7xy - 2y2 + 17x - 26y - 60 = 0 is transformed if the origin is shifted to the point (2, -3), the axes remaining parallel to the original axis.
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Q29. Find the equation of a line which passes through the point (2, 3) and whose x-intercept is twice of y-intercept.
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Q30. Shift the origin to a suitable point so that the equation y2 +4y + 8x - 2 = 0 will not contain term in y and constant term.
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Q31. Determine x so that the line passing through (3, 4) and (x, 5) makes 135° angle with the positive direction of x-axis.
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Q32. Find the equation of a line passing through the point (3, 2) and cuts off intercepts a and b on x- and y-axes such that a - b = 2.
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Q33. Find the equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0.
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Q34. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
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Q35. Find the equation of the straight line which passes through the origin and makes angle 60° with the line
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Q36. A line intersects the straight lines 5x - y - 4 = 0 and 3x - 4y - 4 = 0 atA and B, respectively. If a point P(1, 5) on the line AB is such that AP : PB = 2 : 1 (internally), find point A.
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Q37. If the foot of the perpendicular from the origin to a straight line is at the point (3, -4). Then find the equation of the line.
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Q38. Find the equation of a straight line which makes an angle of
with the positive direction of x-axis and cuts an intercept of 6 units in the negative direction of y-axis.
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Q39. A line passes through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis and is rotated about A in clockwise direction through an angle of 15°. Find the equation of the straight line in the new position.
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Q40. The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anti-clockwise direction through an angle of 15°. Find the equation of a line in the new position.
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Q41. Convert the following equation of a line into normal form. 3x + 4y + 5
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Q42. Reduce into the (i) slope intercept form and also find its slope and y-intercept.(ii) intercept form and also find the lengths of x and y intercepts.(iii) normal form and also find the values of p and ⍺.
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Q43. In what ratio does the line joining the points (2, 3) and (4, 1) divide the segment joining the points (1, 2) and (4, 3)?
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Q44. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points(7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
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Q45. Find the measure of the∠ ABC if the coordinates of A, B and C are A(-2, 1), B(2, 3) and C(-2, -4).
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Q46. Find the equation of a line through (1, 2) that is perpendicular to the line x - 2y + 1 = 0.
x + 2y - 4 = 0
x - 2y - 4 = 0
2x + y - 4 = 0
2x - y - 4 = 0
A
B
C
D
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Q47. The equation of straight line cutting off an intercept -2 from y-axis and being equally inclined to the axes are
y = x + 2, y = x - 2
y = x - 2, y = x - 2
y = -x - 2, y = x - 2
None of these
A
B
C
D
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tan-1(7)
Q48. The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) is
None of these
A
B
C
D
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Q49. Find the angle between the lines
None of these
A
B
C
D
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Q50. Find angles between the lines
35°
45°
30°
60°
A
B
C
D
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Q51. The triangle formed by the lines x + y = 0, 3x + y = 4, x + 3y = 4 is
Isosceles
Right angled
Equilateral
None of these
A
B
C
D
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Q52. Two lines are drawn trough (3, 4) each of which makes angle of 45° with line x - y = 2, then area of the triangle formed by these lines is
9 sq units
2 sq units
A
B
C
D
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Q53. The inclination of the straight line passing through the point (-3, 6) and the mid-point of the line joining the points (4, -5) and (-2, 9) is
A
B
C
D
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Q54. The equations of the lines through (1, 2) which make equal angles with
x = 1, y = 2
x = 2, y = 1
A
B
C
D
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Q55. Find the equations of the lines through the line makes an angle 45° with the line x - 2y = 3.
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Q56. A vertex of an equilateral triangle is (2, 3) and the equation of the opposite side x + y = 2. Find the equation of the other sides of the triangle.
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Q57. A line 4x + y = 1 through the point A(2, -7) meets the line BC, whose equation is 3x - 4y + 1 = 0 at the point B. Find the equation of the line AC so that AB = AC.
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Q58. Find the equations of straight lines passing through (-2, -7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
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Q59. Find the equations of the lines passing through the point (2, 3) and equally inclined to the lines 3x - 4y = 7 and 12x - 5y + 6 = 0.
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Q60. In triangle ABC, equation of the right bisectors of the sides AB and AC arex + y = 0 and y - x = 0 respectively. If A = (5, 7) then find the equation of side BC.
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Q61. The coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x + 4 is given by
A
B
C
D
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(1, -1)
Q62. A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is
(0, 0)
(1, 1)
(0, 1)
A
B
C
D
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Q63. Find the image of the point (4, -13) in the line 5x + y + 6 = 0.
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Q64. Find the foot of the perpendicular from the point (2, 4) upon x + y = 1.
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Q65. The distance of the point of intersection of lines 2x - 3y + 5 = 0 and3x + 4y = 0 from the line 5x - 2y = 0 is
A
B
C
D
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Q66. The length of perpendicular from the point (a cos ⍺, a si ⍺) upon the straight line y = x tan ⍺ + c, c > 0, is
c
c cos ⍺
c sin2 ⍺
c sec2 ⍺
A
B
C
D
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Q67. Equation of the line passing through (1, 2) and parallel to the line y = 3x - 1 is
y + 2 = x + 1
y - 2 = 3(x - 1)
y + 2 = 3(x + 1)
y - 2 = x - 1
A
B
C
D
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Q68. The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to line x - 2y = 1, is
A
B
C
D
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Q69. Find the image of the point (3, 4) with respect to the line y = x.
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Q70. Area of parallelogram whose sides are 2x + y + 1 = 0, 2x + y + 4 = 0,x - 3y - 1 = 0 and x - 3y + 2 = 0 is equal to______.
A
B
C
D
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Q71. If t1 and t
2 are roots of the equation t2 + λt + 1 = 0, where λ is an arbitrary
constant. Then, the line joining the points (at1
2, 2 at1) and (at
22 , 2 at
2 ) always
passes through a fixed point whose coordinates are
(a, 0)
(0, a)
(-a, 0)
(0, -a)
A
B
C
D
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Q72. The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, -7) is 21 sq units. The locus of the point is
6x + y - 32 = 0
x + 6y - 32 = 0
6x - y + 32 = 0
6x - y - 32 = 0
A
B
C
D
![Page 74: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/74.jpg)
Q73. The equations of the respective perpendicular bisectors of sides AB and AC of a Δ ABC are x − y + 5 = 0 and x + 2y = 0. If the coordinates of A are (1, –2), then find the equation of BC.
![Page 75: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/75.jpg)
Q74. A ray of light is sent along the line x - 2y = 3. Upon reaching the line3x - 2y = 5, the ray is reflected from it. Find the equation of the line containing the reflected ray.
![Page 76: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/76.jpg)
Q75. A ray of light passing through the point (1, 2) is reflected on the x-axis at a point P and passes through the point (5, 3). Find the abscissa of the point P.
![Page 77: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/77.jpg)
Q76. Find equation of straight lines passing through (2, 3) and having an intercept of length 2 units between 2x + y = 3 and 2x + y = 5.
![Page 78: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/78.jpg)
Q77. Equation of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are
y = x, y + x = 1
y = x, y + x = 2
y = 2x, y + 2x = 1
A
B
C
D
![Page 79: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/79.jpg)
Q78. Consider the family of lines 5x + 3y - 2 + λ1 (3x - y - 4) = 0 and
x - y + 1 + λ2(2x - y - 2) = 0. Find the equation of a straight line that belongs to
both the families.
![Page 80: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/80.jpg)
Q79. Lines 2x + y = 1 and 2x + y = 7 are
on the same side of a point
same lines
on the opposite side of a point
perpendicular lines
A
B
C
D
![Page 81: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/81.jpg)
Q80. Find the equation of a line which passes through the intersection point of the lines 3x − 4y + 6 = 0 and x + y + 2 = 0, that is farthest from the point P (2, 3).
![Page 82: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/82.jpg)
Q81. The equations of perpendicular bisectors of sides AB and AC of a ΔABC are x - y + 5 = 0 and x + 2y = 0 respectively. If the coordinates of vertex A are (1, -2), then the equation of BC is
23x + 14y - 40 = 0
23x - 14y + 40 = 0
14x - 23y + 40 = 0
14x + 23y - 40 = 0
A
B
C
D
![Page 83: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/83.jpg)
Q82. The equations of the bisector of the acute angle between the lines3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is
99x - 27y - 81 = 0
21x + 77y - 101 = 0
11x - 3y + 9 = 0
21x + 77y + 101 = 0
A
B
C
D
![Page 84: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/84.jpg)
Q83. The equations of bisectors of the angle between the lines |x| = |y| are
y = ±x and x = 0
y = 0 and x = 0
None of these
A
B
C
D
![Page 85: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/85.jpg)
Q84. Find the equation of the bisectors bisecting the angle containing the origin of the straight lines 4x + 3y = 6 and 5x + 12y + 9 = 0.
![Page 86: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/86.jpg)
Q85. Find the bisector of the acute angle between the lines x + y = 3 and 7x - y + 5 = 0.
![Page 87: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/87.jpg)
Q86. Prove that the length of the perpendicular drawn from any point of the line 7x - 9y + 10 = 0 to the lines 3x + 4y = 5 and 12x + 5y = 7 are the same.
![Page 88: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/88.jpg)
Straight Lines DPP- 11th Elite Solutions
![Page 89: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/89.jpg)
Q1. The vertices of a triangle ABC are A(-2, 3), B(2, -1) and C(4, 0). Find cos A.
![Page 90: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/90.jpg)
Solution:
![Page 91: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/91.jpg)
Q2. Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
![Page 92: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/92.jpg)
Solution:
![Page 93: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/93.jpg)
Q3. Find the coordinates of the points which trisect the line segment joining (1, -2) and (-3, 4)
![Page 94: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/94.jpg)
Solution:
![Page 95: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/95.jpg)
Q4. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by the X-axis.
![Page 96: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/96.jpg)
Solution:
![Page 97: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/97.jpg)
Q5. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by x + y - 1 = 0
![Page 98: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/98.jpg)
Solution:
![Page 99: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/99.jpg)
Q6. Find the ratio in which the segment joining the points A(2, -4) and B(4, 5) is divided by 2x + y + 1 = 0.
![Page 100: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/100.jpg)
Solution:
![Page 101: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/101.jpg)
Q7. The coordinates of the midpoints of the sides of a triangle are (1, 1), (3, 2) and (4, 1). Find the coordinates of its vertices.
![Page 102: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/102.jpg)
Solution:
![Page 103: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/103.jpg)
Q8. Determine the ratio in which the line 3x + y - 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
![Page 104: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/104.jpg)
Solution:
![Page 105: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/105.jpg)
Q9. If the midpoints of a triangle are (2, 0), (2, 1) and (0, 1) then find coordinates of its vertices.
![Page 106: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/106.jpg)
P (2, 0)
A (x1, y1)
B (x2, y2) C (x3, y3)Q (2, 1)
R (0, 1)
Solution:
![Page 107: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/107.jpg)
Solution:
![Page 108: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/108.jpg)
Alternate Solution
O
Q (2, 1)(0, 2)
R (0, 1)
P(2, 0) (4, 0)X
Y
Solution:
![Page 109: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/109.jpg)
Q10. Find the orthocentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4).
![Page 110: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/110.jpg)
Solution:
![Page 111: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/111.jpg)
Q11. If the circumcentre of an acute angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and(2a, -2a), then find the orthocentre.
![Page 112: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/112.jpg)
Solution:
![Page 113: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/113.jpg)
Q12. Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, then coordinates of third vertex are
(4, 7)
(-4, 7)
(-4, -7)
None of these
A
B
C
D
![Page 114: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/114.jpg)
Solution:
![Page 115: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/115.jpg)
Q13. Two vertices of a ΔABC are A(0, 0), B(0, 2) and C(2, 0). Find the distance between the circumcentre and orthocentre.
![Page 116: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/116.jpg)
Solution:
![Page 117: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/117.jpg)
Q14. Orthocentre and circumcentre of a ΔABC are (a, b) and (c, d), respectively. If the coordinates of the vertex A are (x
1, y
1), then find the coordinates of the
middle point of BC.
![Page 118: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/118.jpg)
Solution:
![Page 119: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/119.jpg)
Q15. If the coordinates of two points A and B are (3, 4) and (5, -2), respectively. Find the coordinates of any point P if PA = PB and area of ΔPAB = 10 sq. units.
![Page 120: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/120.jpg)
Solution:
![Page 121: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/121.jpg)
Solution:
![Page 122: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/122.jpg)
Q16. If ⍺, β, γ are the roots of the equation x3 - 3px2 + 3qx - 1 = 0, then find the centroid of the triangle whose vertices are (⍺, β + γ), (β, ⍺ + γ), (γ, ⍺ + β)
![Page 123: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/123.jpg)
Solution:
![Page 124: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/124.jpg)
Q17. Find the area of a triangle whose vertices are (t, t + 2), (t + 3, t) and (t + 2, t + 2)
![Page 125: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/125.jpg)
Solution:
![Page 126: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/126.jpg)
Q18. Find the area of a pentagon whose vertices are (4, 3), (-5, 6) (0, 7), (3, -6) and (-7, -2)
![Page 127: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/127.jpg)
Solution:
![Page 128: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/128.jpg)
Q19. Find the value of k if (k + 1, 2 - k), (1 - k, - k) and (2 + k, 3 - k) are collinear.
![Page 129: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/129.jpg)
Solution:
![Page 130: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/130.jpg)
Q20. Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.
![Page 131: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/131.jpg)
Solution:
![Page 132: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/132.jpg)
Q21. The locus of a point which moves such that its distance from the point(0, 0) is twice its distance from the y-axis, is
x2 - y2 = 0
3x2 - y2 = 0
x2 - 3y2 = 0
None of these
A
B
C
D
![Page 133: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/133.jpg)
Solution:
![Page 134: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/134.jpg)
Q22. Find the locus of a point whose coordinates are given by x = 2t3 + t, y = t - 1, where t is a parameter
![Page 135: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/135.jpg)
Solution:
![Page 136: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/136.jpg)
Q23. Find the locus of a movable point P, for which the sum of its distance from (0, 3) and (0, -3) is 8.
![Page 137: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/137.jpg)
Solution:
![Page 138: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/138.jpg)
Solution:
![Page 139: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/139.jpg)
Q24. If P be the mid-point of the straight line joining the points A(1, 2) and Q where Q is a variable point on the curve x2 + y2 + x + y = 0. Find the locus of P.
![Page 140: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/140.jpg)
Solution:
![Page 141: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/141.jpg)
Solution:
![Page 142: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/142.jpg)
Q25. Find the locus of a point such that the sum of its distance from the points (0, 2) and (0, -2) is 6.
![Page 143: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/143.jpg)
Solution:
![Page 144: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/144.jpg)
Q26. Find the equation of the curve 2x2 + y2 - 3x + 5y - 8 = 0, when the origin is shifted to the point (-1, 2) without changing the direction of the axes.
![Page 145: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/145.jpg)
Solution:
![Page 146: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/146.jpg)
Q27. The equation of a curve referred to the new axes retaining their directions and origin is (4, 5) is x2 + y2 = 36. Find the equation referred to the original axes.
![Page 147: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/147.jpg)
Solution:
![Page 148: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/148.jpg)
Q28. Find the equation to which the equation x2 + 7xy - 2y2 + 17x - 26y - 60 = 0 is transformed if the origin is shifted to the point (2, -3), the axes remaining parallel to the original axis.
![Page 149: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/149.jpg)
Solution:
![Page 150: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/150.jpg)
Q29. Find the equation of a line which passes through the point (2, 3) and whose x-intercept is twice of y-intercept.
![Page 151: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/151.jpg)
Solution:
![Page 152: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/152.jpg)
Q30. Shift the origin to a suitable point so that the equation y2 +4y + 8x - 2 = 0 will not contain term in y and constant term.
![Page 153: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/153.jpg)
Solution:
![Page 154: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/154.jpg)
Q31. Determine x so that the line passing through (3, 4) and (x, 5) makes 135° angle with the positive direction of x-axis.
![Page 155: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/155.jpg)
Solution:
![Page 156: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/156.jpg)
Q32. Find the equation of a line passing through the point (3, 2) and cuts off intercepts a and b on x- and y-axes such that a - b = 2.
![Page 157: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/157.jpg)
Solution:
![Page 158: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/158.jpg)
Q33. Find the equation of the straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0.
![Page 159: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/159.jpg)
Solution:
![Page 160: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/160.jpg)
Q34. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
![Page 161: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/161.jpg)
Solution:
![Page 162: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/162.jpg)
Q35. Find the equation of the straight line which passes through the origin and makes angle 60° with the line
![Page 163: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/163.jpg)
Solution:
![Page 164: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/164.jpg)
Solution:
![Page 165: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/165.jpg)
Q36. A line intersects the straight lines 5x - y - 4 = 0 and 3x - 4y - 4 = 0 atA and B, respectively. If a point P(1, 5) on the line AB is such that AP : PB = 2 : 1 (internally), find point A.
![Page 166: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/166.jpg)
Solution:
![Page 167: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/167.jpg)
Q37. If the foot of the perpendicular from the origin to a straight line is at the point (3, -4). Then find the equation of the line.
![Page 168: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/168.jpg)
Solution:
![Page 169: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/169.jpg)
Q38. Find the equation of a straight line which makes an angle of
with the positive direction of x-axis and cuts an intercept of 6 units in the negative direction of y-axis.
![Page 170: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/170.jpg)
Solution:
![Page 171: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/171.jpg)
Q39. A line passes through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis and is rotated about A in clockwise direction through an angle of 15°. Find the equation of the straight line in the new position.
![Page 172: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/172.jpg)
Solution:
![Page 173: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/173.jpg)
Q40. The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anti-clockwise direction through an angle of 15°. Find the equation of a line in the new position.
![Page 174: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/174.jpg)
Solution:
![Page 175: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/175.jpg)
Q41. Convert the following equation of a line into normal form. 3x + 4y + 5
![Page 176: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/176.jpg)
Solution:
![Page 177: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/177.jpg)
Q42. Reduce into the (i) slope intercept form and also find its slope and y-intercept.(ii) intercept form and also find the lengths of x and y intercepts.(iii) normal form and also find the values of p and ⍺.
![Page 178: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/178.jpg)
Solution:
![Page 179: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/179.jpg)
Q43. In what ratio does the line joining the points (2, 3) and (4, 1) divide the segment joining the points (1, 2) and (4, 3)?
![Page 180: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/180.jpg)
Solution:
![Page 181: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/181.jpg)
Q44. If the straight line, 2x - 3y + 17 = 0 is perpendicular to the line passing through the points(7, 17) and (15, β), then β equals
5
-5
JEE Main - 2019A
B
C
D
![Page 182: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/182.jpg)
Solution:
![Page 183: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/183.jpg)
Q45. Find the measure of the∠ ABC if the coordinates of A, B and C are A(-2, 1), B(2, 3) and C(-2, -4).
![Page 184: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/184.jpg)
Solution:
![Page 185: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/185.jpg)
Q46. Find the equation of a line through (1, 2) that is perpendicular to the line x - 2y + 1 = 0.
x + 2y - 4 = 0
x - 2y - 4 = 0
2x + y - 4 = 0
2x - y - 4 = 0
A
B
C
D
![Page 186: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/186.jpg)
Solution:
![Page 187: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/187.jpg)
Q47. The equation of straight line cutting off an intercept -2 from y-axis and being equally inclined to the axes are
y = x + 2, y = x - 2
y = x - 2, y = x - 2
y = -x - 2, y = x - 2
None of these
A
B
C
D
![Page 188: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/188.jpg)
Solution:
![Page 189: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/189.jpg)
Solution:
![Page 190: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/190.jpg)
tan-1(7)
Q48. The angle between the line x + y = 3 and the line joining the points (1, 1) and (-3, 4) is
None of these
A
B
C
D
![Page 191: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/191.jpg)
Solution:
![Page 192: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/192.jpg)
Q49. Find the angle between the lines
None of these
A
B
C
D
![Page 193: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/193.jpg)
Solution:
![Page 194: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/194.jpg)
Q50. Find angles between the lines
35°
45°
30°
60°
A
B
C
D
![Page 195: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/195.jpg)
Solution:
![Page 196: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/196.jpg)
Q51. The triangle formed by the lines x + y = 0, 3x + y = 4, x + 3y = 4 is
Isosceles
Right angled
Equilateral
None of these
A
B
C
D
![Page 197: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/197.jpg)
Solution:
![Page 198: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/198.jpg)
Q52. Two lines are drawn trough (3, 4) each of which makes angle of 45° with line x - y = 2, then area of the triangle formed by these lines is
9 sq units
2 sq units
A
B
C
D
![Page 199: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/199.jpg)
Solution:
![Page 200: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/200.jpg)
Q53. The inclination of the straight line passing through the point (-3, 6) and the mid-point of the line joining the points (4, -5) and (-2, 9) is
A
B
C
D
![Page 201: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/201.jpg)
Solution:
![Page 202: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/202.jpg)
Q54. The equations of the lines through (1, 2) which make equal angles with
x = 1, y = 2
x = 2, y = 1
A
B
C
D
![Page 203: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/203.jpg)
Solution:
![Page 204: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/204.jpg)
Q55. Find the equations of the lines through the line makes an angle 45° with the line x - 2y = 3.
![Page 205: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/205.jpg)
Solution:
![Page 206: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/206.jpg)
Q56. A vertex of an equilateral triangle is (2, 3) and the equation of the opposite side x + y = 2. Find the equation of the other sides of the triangle.
![Page 207: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/207.jpg)
Solution:
![Page 208: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/208.jpg)
Solution:
![Page 209: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/209.jpg)
Q57. A line 4x + y = 1 through the point A(2, -7) meets the line BC, whose equation is 3x - 4y + 1 = 0 at the point B. Find the equation of the line AC so that AB = AC.
![Page 210: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/210.jpg)
Solution:
![Page 211: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/211.jpg)
Q58. Find the equations of straight lines passing through (-2, -7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
![Page 212: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/212.jpg)
Solution:
![Page 213: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/213.jpg)
Q59. Find the equations of the lines passing through the point (2, 3) and equally inclined to the lines 3x - 4y = 7 and 12x - 5y + 6 = 0.
![Page 214: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/214.jpg)
Solution:
![Page 215: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/215.jpg)
Solution:
![Page 216: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/216.jpg)
Q60. In triangle ABC, equation of the right bisectors of the sides AB and AC arex + y = 0 and y - x = 0 respectively. If A = (5, 7) then find the equation of side BC.
![Page 217: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/217.jpg)
Solution:
![Page 218: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/218.jpg)
Q61. The coordinates of the foot of perpendicular from the point (2, 3) on the line y = 3x + 4 is given by
A
B
C
D
![Page 219: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/219.jpg)
Solution:
![Page 220: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/220.jpg)
(1, -1)
Q62. A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is
(0, 0)
(1, 1)
(0, 1)
A
B
C
D
![Page 221: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/221.jpg)
Solution:
![Page 222: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/222.jpg)
Q63. Find the image of the point (4, -13) in the line 5x + y + 6 = 0.
![Page 223: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/223.jpg)
Solution:
![Page 224: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/224.jpg)
Q64. Find the foot of the perpendicular from the point (2, 4) upon x + y = 1.
![Page 225: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/225.jpg)
Solution:
![Page 226: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/226.jpg)
Q65. The distance of the point of intersection of lines 2x - 3y + 5 = 0 and3x + 4y = 0 from the line 5x - 2y = 0 is
A
B
C
D
![Page 227: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/227.jpg)
Solution:
![Page 228: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/228.jpg)
Q66. The length of perpendicular from the point (a cos ⍺, a si ⍺) upon the straight line y = x tan ⍺ + c, c > 0, is
c
c cos ⍺
c sin2 ⍺
c sec2 ⍺
A
B
C
D
![Page 229: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/229.jpg)
Solution:
![Page 230: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/230.jpg)
Q67. Equation of the line passing through (1, 2) and parallel to the line y = 3x - 1 is
y + 2 = x + 1
y - 2 = 3(x - 1)
y + 2 = 3(x + 1)
y - 2 = x - 1
A
B
C
D
![Page 231: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/231.jpg)
Solution:
![Page 232: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/232.jpg)
Q68. The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to line x - 2y = 1, is
A
B
C
D
![Page 233: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/233.jpg)
Solution:
![Page 234: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/234.jpg)
Q69. Find the image of the point (3, 4) with respect to the line y = x.
![Page 235: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/235.jpg)
Solution:
![Page 236: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/236.jpg)
Q70. Area of parallelogram whose sides are 2x + y + 1 = 0, 2x + y + 4 = 0,x - 3y - 1 = 0 and x - 3y + 2 = 0 is equal to______.
A
B
C
D
![Page 237: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/237.jpg)
Solution:
![Page 238: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/238.jpg)
Q71. If t1 and t
2 are roots of the equation t2 + λt + 1 = 0, where λ is an arbitrary
constant. Then, the line joining the points (at1
2, 2 at1) and (at
22 , 2 at
2 ) always
passes through a fixed point whose coordinates are
(a, 0)
(0, a)
(-a, 0)
(0, -a)
A
B
C
D
![Page 239: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/239.jpg)
Solution:
![Page 240: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/240.jpg)
Q72. The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, -7) is 21 sq units. The locus of the point is
6x + y - 32 = 0
x + 6y - 32 = 0
6x - y + 32 = 0
6x - y - 32 = 0
A
B
C
D
![Page 241: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/241.jpg)
Solution:
![Page 242: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/242.jpg)
Q73. The equations of the respective perpendicular bisectors of sides AB and AC of a Δ ABC are x − y + 5 = 0 and x + 2y = 0. If the coordinates of A are (1, –2), then find the equation of BC.
![Page 243: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/243.jpg)
Solution:
![Page 244: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/244.jpg)
Q74. A ray of light is sent along the line x - 2y = 3. Upon reaching the line3x - 2y = 5, the ray is reflected from it. Find the equation of the line containing the reflected ray.
![Page 245: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/245.jpg)
Solution:
![Page 246: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/246.jpg)
Solution:
![Page 247: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/247.jpg)
Q75. A ray of light passing through the point (1, 2) is reflected on the x-axis at a point P and passes through the point (5, 3). Find the abscissa of the point P.
![Page 248: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/248.jpg)
Solution:
![Page 249: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/249.jpg)
Q76. Find equation of straight lines passing through (2, 3) and having an intercept of length 2 units between 2x + y = 3 and 2x + y = 5.
![Page 250: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/250.jpg)
A
BC
(2, 3)
22x + y = 3
2x + y = 5
θ
Solution:
![Page 251: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/251.jpg)
Q77. Equation of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are
y = x, y + x = 1
y = x, y + x = 2
y = 2x, y + 2x = 1
A
B
C
D
![Page 252: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/252.jpg)
Solution:
![Page 253: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/253.jpg)
Q78. Consider the family of lines 5x + 3y - 2 + λ1 (3x - y - 4) = 0 and
x - y + 1 + λ2(2x - y - 2) = 0. Find the equation of a straight line that belongs to
both the families.
![Page 254: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/254.jpg)
Solution:
![Page 255: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/255.jpg)
Q79. Lines 2x + y = 1 and 2x + y = 7 are
on the same side of a point
same lines
on the opposite side of a point
perpendicular lines
A
B
C
D
![Page 256: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/256.jpg)
Solution:
![Page 257: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/257.jpg)
Q80. Find the equation of a line which passes through the intersection point of the lines 3x − 4y + 6 = 0 and x + y + 2 = 0, that is farthest from the point P (2, 3).
![Page 258: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/258.jpg)
Solution:
![Page 259: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/259.jpg)
Q81. The equations of perpendicular bisectors of sides AB and AC of a ΔABC are x - y + 5 = 0 and x + 2y = 0 respectively. If the coordinates of vertex A are (1, -2), then the equation of BC is
23x + 14y - 40 = 0
23x - 14y + 40 = 0
14x - 23y + 40 = 0
14x + 23y - 40 = 0
A
B
C
D
![Page 260: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/260.jpg)
Solution:
![Page 261: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/261.jpg)
Solution:
![Page 262: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/262.jpg)
Q82. The equations of the bisector of the acute angle between the lines3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is
99x - 27y - 81 = 0
21x + 77y - 101 = 0
11x - 3y + 9 = 0
21x + 77y + 101 = 0
A
B
C
D
![Page 263: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/263.jpg)
Solution:
![Page 264: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/264.jpg)
Q83. The equations of bisectors of the angle between the lines |x| = |y| are
y = ±x and x = 0
y = 0 and x = 0
None of these
A
B
C
D
![Page 265: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/265.jpg)
Solution:
![Page 266: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/266.jpg)
Q84. Find the equation of the bisectors bisecting the angle containing the origin of the straight lines 4x + 3y = 6 and 5x + 12y + 9 = 0.
![Page 267: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/267.jpg)
Solution:
![Page 268: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/268.jpg)
Q85. Find the bisector of the acute angle between the lines x + y = 3 and 7x - y + 5 = 0.
![Page 269: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/269.jpg)
Solution:
![Page 270: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/270.jpg)
Q86. Prove that the length of the perpendicular drawn from any point of the line 7x - 9y + 10 = 0 to the lines 3x + 4y = 5 and 12x + 5y = 7 are the same.
![Page 271: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/271.jpg)
Solution:
![Page 272: Straight lines DPP -11th Elite](https://reader030.vdocuments.site/reader030/viewer/2022012809/61be47cd24336f37714dd6f9/html5/thumbnails/272.jpg)
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