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Student Book - Series K-1

Coordinate Geometry

Mathletics Instant

Workbooks

(x1, x2)

(y1, y2)

Coordinate geometryStudent Book - Series K

Contents

Topics

Topic 1 - The midpoint of an interval __/__/__ Date completed

Topic 2 - The midpoint formula __/__/__ Topic 3 - Finding the endpoint __/__/__ Topic 4 - The distance between two points __/__/__ Topic 5 - The distance formula __/__/__ Topic 6 - The gradient of a line __/__/__

Topic 8 - Different forms of linear equations __/__/__ Topic 9 - Determining whether or not a point lies on a line __/__/__

Topic 7 - The gradient formula __/__/__

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__

Coordinate geometryMathletics Instant Workbooks – Series K Copyright © 3P Learning

Coordinate geometry

Coordinate geometryMathletics Instant Workbooks – Series K Copyright © 3P Learning 1

QUESTION 1a What number is halfway between 6 and 10? _________________________________________________b What is the average of 6 and 10? __________________________________________________________c Find 6 + 10 ___________________________________________________________________________2d What number is halfway between –2 and 12? ________________________________________________e What is the average of –2 and 12? _________________________________________________________f Find –2 + 12 __________________________________________________________________________2

QUESTION 2 What number is halfway between the point A and the point B on each number line?a _______ b _______

c _______ d _______

QUESTION 3 Find the number that is halfway between:a 0 and 16 = ______________ b 4 and 12 = ______________ c 2 and 10 = ______________d 3 and 15 = ______________ e 1 and 13 = ______________ f –1 and 7 = ______________g –2 and 6 = ______________ h –4 and 4 = ______________ i 2 and 18 = ______________j –5 and 15 = ______________ k 3 and 17 = ______________ l 1 and 19 = ______________

QUESTION 4 Consider the points P(4, 10) and Q(6 and –2).a Use the x-coordinates of the points P and Q to find the number halfway between 4 and 6 _____________

_____________________________________________________________________________________b Use the y-coordinates of the points P and Q to find the number halfway between 10 and –2 ___________

_____________________________________________________________________________________c What are the coordinates of the point M, which is halfway between P and Q? _______________________

_____________________________________________________________________________________

QUESTION 5 If x1 and x2 are given, find the value of x when x = x1 + x22

a x1 = 3 and x2 = 21 ___________________ b x1 = –2 and x2 = 8 ___________________c x1 = 5 and x2 = 13 ___________________ d x1 = 4 and x2 = 10 ___________________e x1 = 1 and x2 = 9 ___________________ f x1 = –6 and x2 = 14 ___________________g x1 = – 4 and x2 = 8 ___________________ h x1 = –6 and x2 = 10 ___________________i x1 = –5 and x2 = 7 ___________________ j x1 = –2 and x2 = 16 ___________________k x1 = –7 and x2 = –1 ___________________ l x1 = –8 and x2 = –2 ___________________

26 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1

ANSWERS

page 150

CHAPTER 3Coordinate geometry

UNIT 1: The midpoint of an interval

0 1 2 3 4

A B

5 6 7••

0 1A B

2 3 4 5 6 7• •–2 –1

BA0 1 2 3 4 5••

–1 0BA

1 2 3 4 5 6••

Topic 1 - The midpoint of an interval

Coordinate geometry


QUESTION 1 Use the midpoint formula x = x1 + x2 and y = y1 + y2 to find the midpoint of the interval2 2joining each of the following sets of points.

a A(0, 6), B(0, 10) ___________________ b A(2, 7), B(8, 9) ___________________c C(–2, –5), D(–7, 9) ___________________ d E(4, 9), F(8, 3) ___________________e G(8, 8), H(6, 0) ___________________ f I(0, 8), J(4, 4) ___________________

QUESTION 2 Use the midpoint formula to find the midpoints of the intervals joining the followingpoints:

a P(2, –5), Q(8, 5) ___________________ b R(9, 3), S(7, 5) ___________________c A(5, 13), B(11, 11) ___________________ d C(4, 5), D(6, 9) ___________________e E(–3, –6), F(1, 4) ___________________ f G(–4, 6), H(8, –2) ___________________

QUESTION 3 The points O(0, 0), A(1, 4), B(6, 4) and C(5, 0) are the vertices of a parallelogram.a Find the coordinates of the midpoint of OB. _________________________________________________

_____________________________________________________________________________________b Find the coordinates of the midpoint of AC. _________________________________________________

_____________________________________________________________________________________c Are the midpoints of OB and AC the same? _________________________________________________

_____________________________________________________________________________________d What can you say about the diagonals of the parallelogram? ____________________________________

_____________________________________________________________________________________

QUESTION 4 Find the coordinates of the centre of the circle if the endpoints of a diameter are:a A(–2, 9), B(9, 6) ___________________ b C(6, 0), D(4, 2) ___________________c E(3, 11), F(9, 9) ___________________ d G(5, 6), H(7, 10) ___________________e I(–5, –8), J(–1, 2) ___________________ f K(–5, 5), L(7, –3) ___________________

QUESTION 5 The vertices of a triangle ABC are A(2, 13), B(14, 15) and C(–3, 5). Find the midpointof each side.

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

QUESTION 6 Prove that the midpoint of A(5, –8) and B(–5, 8) is the origin.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Coordinate geometryUNIT 2: The midpoint formula

Chapter 3: Coordinate geometry 27

ANSWERS

page 150

Topic 2 - The midpoint formula

Coordinate geometry


QUESTION 1 For each diagram, find the coordinates of A, given that M is the midpoint of AB.a ________________ b ________________

________________ ________________________________ ________________________________ ________________

QUESTION 2 The coordinates of the midpoint M of an interval and one of its endpoints A, are given.Find the coordinates of the other endpoint B.

a M(4, 7) and A(1, 6) ____________________ b M(5, 9) and A(1, 7) ____________________

c M(6, –3) and A(4, 1) ___________________ d M(0, 8) and A(4, 10) ___________________

e M(5, 9) and A(1, 7) ____________________ f M(4, 3) and A(0, 0) ____________________

g M(3, 9) and A(–1, 5) ___________________ h M(7, 9) and A(4, 5) ____________________

i M(2, 1) and A(5, –5) ___________________ j M(4, 9) and A(0, 2) ____________________

k M(8, 4) and A(5, 2) ____________________ l M(8, 0) and A(7, 3) ____________________

QUESTION 3 Given the coordinates of the centre C, of a circle, and one endpoint B, of a diameter,find the coordinates of the other endpoint A, of the diameter.

a C(2, 4) and B(0, 1) ____________________ b C(3, 7) and B(2, 6) ____________________

c C(–1, 2) and B(–4, 4) ___________________ d C(–2, 5) and B(–6, 4) ___________________

e C(0, 0) and B(–4, –6) ___________________ f C(6, 9) and B(4, 6) ____________________

g C(–1, 8) and B(–4, 3) ___________________ h C(–3, 1) and B(–7, 0) ____________________

QUESTION 4

a (3, 6) is the midpoint of AB and A is the point (0, 2). Find the coordinates of B. ________________________________________________________________________________________________________

b If the midpoint of (a, b) and (9, 9) is (6, 2). What are the values of a and b?_____________________________________________________________________________________________________________

c if the midpoint of (5, p) and (7, –4) is (6, 3). What is the value of p? __________________________________________________________________________________________________________________

d If the midpoint of (x, 5) and (9, y) is (1, 6). What are the values of x and y? _____________________________________________________________________________________________________________

Coordinate geometryUNIT 3: Finding an endpoint


ANSWERS

page 150

••

• A

BM(–4, 1)

(–1, 3)

•

•

•

A

B

M (0, 2)

3, –2)

Yr 10 Maths 1.qxd:Yr 10 Maths 1.qxd 14/1/09 10:23 AM Page 28

Topic 3 - Finding the endpoint

Coordinate geometry


QUESTION 1 Plot each pair of points on number planes. Then calculate the distance between them.a A(3, 6) and B(7, 6), AB = ________________________b C(5, 2) and D(5, 7), CD = ________________________c E(–3, 5) and F(–3, 0), EF = ________________________d G(5, 4) and H(9, 4), GH = ________________________e I(7, 2) and J(11, 2), IJ = ________________________f K(–1, 2) and L(2, 2), KL = ________________________g M(1, 1) and N(1, 8), MN = ________________________h O(4, 4) and P(4, 9), OP = ________________________

QUESTION 2 Use Pythagoras’ theorem to find the distance AB in each diagram. Leave your answersin surd (square root) form where necessary.

a b c

______________________ ______________________ ______________________

QUESTION 3 Use Pythagoras’ theorem to find the length of each interval. Leave your answers insurd form where necessary.

a b c

______________________ ______________________ ______________________

QUESTION 4 ABCD is a rectangle. Find:a The coordinates of the vertex A. ____________________b The length of the interval:

i AB ____________________ii BC ____________________iii CD ____________________iv DA ____________________v BD ____________________vi AC ____________________

c The perimeter of ABCD. _________________________________________________________________d The area of ABCD. _____________________________________________________________________

Coordinate geometryUNIT 4: The distance between two points


ANSWERS

page 150

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6 •

•

B (4, 6)

A (0, 0)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6

•

•

B (2, 2)

A (–3, –2)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6

•

•

B (–6, 2)

A (1, –2)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6

•

•

B (5 –2)

A (–3, 4)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6 •

•

B (5, 6)

A (1, 1)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6

•

•

B (4, 4)

A (–5, –2)

y

x0–2 2 4 6–4–6

2

–2

–4

–6

4

6A B (2, 4)

C (2, –2)D (–3, –2)

Yr 10 Maths 1.qxd:Yr 10 Maths 1.qxd 14/1/09 10:23 AM Page 29

Topic 4 - The distance between two points

Coordinate geometry


QUESTION 1 Use the distance formula d = �(x2 – x1)2 + (y2 – y1)2 to calculate the distance betweenthe following pairs of points. Leave your answer in surd form if necessary.

a A(1, 3) and B(5, 7) ____________________ b A(4, 2) and B(11, 1) ____________________

c C(–2, 3) and D(5, 2) ___________________ d E(5, 1) and F(8, 2) ___________________

e G(3, 9) and H(5, 12) ____________________ f I(3, 8) and J(2, 5) ____________________

QUESTION 2 Calculate the distance between the following pairs of points correct to one decimal place.

a A(5, 8) and B(–1, –2) ___________________ b C(4, 9) and D(9, 5) ____________________

c E(6, 7) and F(0, –2) ___________________ d G(3, 7) and H(9, 15) ___________________

e I(5, 6) and J(7, 10) ____________________ f K(1, 6) and L(2, 5) ____________________

QUESTION 3

a Find the exact distance between the points A(–3, 4) and B(1, 9) and then square it. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b Find the perimeter of the triangle whose vertices are A(6, 0), B(9, 6) and C(1, 0). __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

QUESTION 4 The points A(–2, 3), B(5, 3), C(5, –1) and D(–2, –1) are the vertices of a rectangle.Find:

a the length AB = ________________________________________________________________________b the length BC = ________________________________________________________________________c the length CD = ________________________________________________________________________d the length DA = ________________________________________________________________________e the exact length AC = ___________________________________________________________________f the exact length BD = ___________________________________________________________________

Coordinate geometryUNIT 5: The distance formula


ANSWERS

page 151

Topic 5 - The distance formula

Coordinate geometry


QUESTION 1 State whether the gradient of the line � is positive or negative.a b c d

QUESTION 2 Find the gradient of each line.a b c

______________________ ______________________ ____________________________________________ ______________________ ____________________________________________ ______________________ ______________________

d e f

______________________ ______________________ ____________________________________________ ______________________ ____________________________________________ ______________________ ______________________

g h i

______________________ ______________________ ____________________________________________ ______________________ ____________________________________________ ______________________ ______________________

Coordinate geometryUNIT 6: The gradient of a line


ANSWERS

page 151

�

y

x

�

y

x

�

y

x�

y

x

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

••

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

•

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65•

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

••

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

•

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65 •

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

•

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

•

•

y

x0–2–3 21 43 65–4–5–6

21

–2–1

–3–4–5–6

43

65

•

•

Topic 6 - The gradient of a line

Coordinate geometry


QUESTION 1 Use the gradient formula m = y2 – y1 to find the gradient of the straight line passingx2 – x1through:

a A(3, 5) and B(7, –1) ___________________ b C(2, 5) and D(–2, 1) ____________________

c E(0, 7) and F(4, 3) ____________________ d G(1, –1) and H(6, 4) ___________________

e I(1, 0) and J(4, 9) ____________________ f K(0, 0) and L(5, 8) ____________________

QUESTION 2 Find the gradient of the line between:

a A(–2, –3) and B(3, 2) ___________________ b C(0, 5) and D(5, 0) ____________________

c E(6, 0) and F(1, –5) ____________________ d G(5, 5) and H(2, –5) ___________________

e I(4, 3) and J(1, 4) ____________________ f K(6, 8) and L(1, –1) ____________________

QUESTION 3 Show that A(0, –5), B(3, 1) and C(–2, –9) are collinear.___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

QUESTION 4 A line passes through the points A(1, 3) and B(x, 7) and its gradient is 1.Find the value of x.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

QUESTION 5 Show that the four points A(–2, –3), B(–5, 2), C(0, 4) and D(3, –1) are the vertices of aparallelogram.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

QUESTION 6 Which of the following sets of points is collinear?a (3, 7), (0, 4) and (8, 2) __________________________________________________________________

b (0, 1), (–1, –1) and (2, 5) ________________________________________________________________

Coordinate geometryUNIT 7: The gradient formula


ANSWERS

page 151

Topic 7 - The gradient formula

Coordinate geometry


QUESTION 1 Write each of the following equations in general form:

a 3x + 5y = 9 ___________ b 2x – y = 7 ___________ c y = 3x – 4 ____________

d 4x – 3y = 8 ___________ e 9x – y = 7 ___________ f y = –2x – 6 ___________

g 9x – 5 = 7y ___________ h 4x – 13y = –18 ___________ i y = x5 + 2 ___________

QUESTION 2 Write each of the following equations in the gradient-intercept form:

a 10 + y = 6x ___________ b 4y = 8x + 32 ___________ c 3y = –2x + 1 ____________

d 6y – 3x = 12 ___________ e y + 5x = 0 ___________ f 9x – 4y = 12 ___________

g x + y = 2 ___________ h 3x – 2y = 7 ___________ i 4y = 3x – 8 ___________

QUESTION 3 Write down the gradient (m) and the y-intercept (b) for each of the following:

a y = 3x + 1 ___________ b y = 9x – 5 ___________ c y = –x – 3 ____________

d y = –4x + 7 ___________ e y = 23x – 5 ___________ f y = 1

4x – 2 ___________

QUESTION 4 Write the equation of the line in the gradient-intercept form when the gradient (m) andthe y-intercept (b) are given:

a m = 3, b = 2 ___________ b m = 9, b = –3 ___________ c m = –1, b = 7 ____________

d m = 34, b = 5 ___________ e m = –2

3, b = 1 ___________ f m = –7, b = 8 ___________

QUESTION 5 Write the equation in the form y = mx + b of the line that passes through the given pointand has the given gradient:

a A(–3, 2), m = 4 ___________ b A(4, –1), m = 2 ___________ c A(1, 5), m = 12 ___________

d A(1, 8), m = 23 ___________ e A(2, 5), m = –1

3 ___________ f A(0, 8), m = –3 ___________

Coordinate geometryUNIT 8: Different forms of linear equations


ANSWERS

page 151

Topic 8 - Different forms of linear equations

Coordinate geometry


Topic 9 - Determining whether or not a point lies on a line

QUESTION 1

a Show that the point (–2, 3) lies on the line y = x + 5 __________________________________________

_____________________________________________________________________________________

b Does the point (0, –3) lie on the line 3x – 2y = 6? _____________________________________________

_____________________________________________________________________________________

c Show that the line 2x – y + 3 = 0 passes through the points (0, 3), (2, 7) and (–4, –5) ________________

_____________________________________________________________________________________

QUESTION 2 State whether the point given after each linear equation lies on that line:a 2x + y = 4 (1, 2) _______________________ b 3x – y = 6 (0, –6) ______________________

c y = 4x – 5 (–1, –9) _____________________ d 3x – 4y = 12 (4, –2) ____________________

e 2x + 5y = 10 (0, 2) _____________________ f y = –2x + 3 (–2, 1) _____________________

QUESTION 3 Which of the following lines pass through the origin (0, 0)?a 3x – 4y = 12 ___________________________ b 7x – 2y = 0 _____________________________

c 9x = 4y _______________________________ d 2x – 7y = 8 _____________________________

e y = –5x _______________________________ f y = 4x – 7 _____________________________

QUESTION 4 Find the missing coordinates to make each of the following points satisfy the equationy = 2x – 5:

a (0, ) _______________ b ( , –1) _______________ c (3, ) ________________

d (–2, ) _______________ e (1, ) _______________ f ( , 5) _______________

QUESTION 5

a If the point (–3, –5) lies on the line px – y + 4 = 0 what is the value of p? _________________________

_____________________________________________________________________________________

b The straight line y = mx + 6 passes through the point (–3, 3). Find the value of m ___________________

_____________________________________________________________________________________

Coordinate geometryUNIT 9: Determining whether or not a point lies on a line


ANSWERS

page 151

Total marks achieved for PART A 15

Coordinate geometryTopic Test PART A

Marks

10Coordinate geometry

Mathletics Instant Workbooks – Series K Copyright © 3P Learning

TOPIC TEST PART ACoordinate geometryTime allowed: 15 minutes Total marks = 15

1 What is the gradient of the line that passes through the points (0, 5) and (2, 9)?�A 3 �B –3 �C 2 �D 4

2 What is the slope of the line y = 13x + 5?

�A 5 �B 13 �C –5 �D –1

3

3 The gradient of the line 2x – 5y = 10 is:�A 2 �B 5 �C 2

5 �D 52

4 The point (9, –1) lies on the line:�A 3x + y – 6 = 0 �B 3x – y + 6 = 0 �C x + 3y – 6 = 0 �D x + 3y + 6 = 0

5 The distance between the two points A(0, 2) and B(8, 8) is:�A 6 �B 8 �C 10 �D 12

6 The equation 2y – 3x = 6 expressed in the general form is:�A 2y – 3x + 6 = 0 �B 2y – 3x – 6 = 0 �C –3x + 2y – 6 = 0 �D 3x – 2y + 6 = 0

7 The equation 6x – y = 7 expressed in the gradient-intercept form is:�A 6x = y + 7 �B y = 6x + 7 �C y = 6x – 7 �D y = –6x + 7

8 The midpoint of the interval joining the points (1, –3) and (–3, 5) is:�A (1, –1) �B (–1, 1) �C (1, 1) �D (–1, –1)

9 What is the gradient of the line represented by the equation 3x – 5y = 5?�A 3

5 �B 53 �C 3 �D –5

10 The distance between the points (2, 8) and (–1, 3) is:�A ��26 �B ��122 �C ��34 �D ��130

11 The line y = 5x passes through the point:�A (0, –1) �B (0, 0) �C (0, 1) �D (1, 0)

12 Find the distance between the origin and the point (12, 5).�A ��119 �B 5 �C 12 �D 13

13 Find the gradient of the line represented by the equation 2x + 2y – 12 = 0.

�A –12 �B 1

2 �C –1 �D 1

14 Write y = 3x – 4 in general form.�A y – 3x = –4 �B y + 4 = 3x �C y – 3x + 4 = 0 �D 3x – y – 4 = 0

15 Write 4y – 3x = 12 in the gradient-intercept form.�A y = 3

4 x – 3 �B y = = 34 x + 3 �C y = –3

4 x – 3 �D y = = –34 x + 3

Total marks for PART A 15

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

ANSWERS

page 151


TOPIC TEST PART ACoordinate geometryTime allowed: 15 minutes Total marks = 15

1 What is the gradient of the line that passes through the points (0, 5) and (2, 9)?�A 3 �B –3 �C 2 �D 4

2 What is the slope of the line y = 13x + 5?

�A 5 �B 13 �C –5 �D –1

3

3 The gradient of the line 2x – 5y = 10 is:�A 2 �B 5 �C 2

5 �D 52

4 The point (9, –1) lies on the line:�A 3x + y – 6 = 0 �B 3x – y + 6 = 0 �C x + 3y – 6 = 0 �D x + 3y + 6 = 0

5 The distance between the two points A(0, 2) and B(8, 8) is:�A 6 �B 8 �C 10 �D 12

6 The equation 2y – 3x = 6 expressed in the general form is:�A 2y – 3x + 6 = 0 �B 2y – 3x – 6 = 0 �C –3x + 2y – 6 = 0 �D 3x – 2y + 6 = 0

7 The equation 6x – y = 7 expressed in the gradient-intercept form is:�A 6x = y + 7 �B y = 6x + 7 �C y = 6x – 7 �D y = –6x + 7

8 The midpoint of the interval joining the points (1, –3) and (–3, 5) is:�A (1, –1) �B (–1, 1) �C (1, 1) �D (–1, –1)

9 What is the gradient of the line represented by the equation 3x – 5y = 5?�A 3

5 �B 53 �C 3 �D –5

10 The distance between the points (2, 8) and (–1, 3) is:�A ��26 �B ��122 �C ��34 �D ��130

11 The line y = 5x passes through the point:�A (0, –1) �B (0, 0) �C (0, 1) �D (1, 0)

12 Find the distance between the origin and the point (12, 5).�A ��119 �B 5 �C 12 �D 13

13 Find the gradient of the line represented by the equation 2x + 2y – 12 = 0.

�A –12 �B 1

2 �C –1 �D 1

14 Write y = 3x – 4 in general form.�A y – 3x = –4 �B y + 4 = 3x �C y – 3x + 4 = 0 �D 3x – y – 4 = 0

15 Write 4y – 3x = 12 in the gradient-intercept form.�A y = 3

4 x – 3 �B y = = 34 x + 3 �C y = –3

4 x – 3 �D y = = –34 x + 3

Total marks for PART A 15

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

ANSWERS

page 151


Time allowed: 15 minutes Total marks = 15

Coordinate geometryTopic Test PART B

11Coordinate geometry

Mathletics Instant Workbooks – Series K Copyright © 3P Learning

Total marks achieved for PART B 15

Marks

Time allowed: 15 minutes Total marks = 15

Answers


TOPIC TEST PART BCoordinate geometryTime allowed: 15 minutes Total marks = 15

Question 1 For the points A(–2, 6) and B(3, 5) find:a The distance AB (in surd form). ___________________________b The midpoint of AB. ___________________________c The gradient of AB. ___________________________d If the equation of the line AB is x + 5y = 28. Write this

equation in the general form. ___________________________e Write the equation of the line AB in the gradient-intercept

form. ___________________________

Question 2

a Use Pythagoras’ theorem to find the length of a diagonal of a5 cm by 5 cm square (correct to one decimal place). ___________________________

b Find the distance between the point A(–3, 5) and B(1, 9) andthen square it. ___________________________

c Find the exact distance between the origin and the point (4, 8). ___________________________d Prove that the midpoint of (–5, 7) and (5, –7) is the origin. ___________________________e The coordinates of the midpoint of AB are (2, 2). if A is the

point (–1, –3), what are the coordinates of B? ___________________________

Question 3

a Show that A(0, –4), B(1, –2) and C(–3, –10) are collinear. ___________________________b If the endpoints of the diameter of a circle are (–3, 4) and

(7, 6), what are the coordinates of the centre? ___________________________c The midpoint of P(2, 8) and Q(a, b) is M(4, –4). Find the

coordinates of point Q. ___________________________d Which of the points (–2, –2) and (2, 2) lies on the line

y = 5x – 8? ___________________________e Find the equation of the line that has gradient –2

3 andy-intercept of 6. ___________________________

Total marks for PART B 15

111

1

1

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form. ___________________________

Question 2





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form. ___________________________

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coordinate geometry - moreeinfo.com resources... · coordinate geometry unit 3: finding an endpoint...

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