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Mathletics Instant

Workbooks

Copyright ©

Mathletics Instant

Workbooks

Mathletics Instant

Workbooks

Student Book - Series J-2

Coordinate Geometry

(x1, x2)

(y1, y2)

Coordinate geometryStudent Book - Series J 2

Contents

Topics

Topic 1 - The distance formula __/__/__ Date completed

Topic 2 - The mid-point of an interval __/__/__ Topic 3 - Different forms of linear equations __/__/__ Topic 4 - Graphing straight lines __/__/__ Topic 5 - The gradient of a straight line __/__/__ Topic 6 - Using the point–gradient formula to find the

equation of a line __/__/__

Topic 8 - Parallel and perpendicular lines __/__/__

Topic 7 - Using the two-point formula to find the equation of a line __/__/__

Coordinate geometryMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

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

1

Coordinate geometry


Topic 1 - The distance formula

47Chapter 6: Coordinate geometry

Coordinate geometryCHAPTER 6

UNIT 1: The distance formula

EXCEL YEARS 9 & 10 ADVANCED MATHS

Page 79

QUESTION 1 Calculate the distance between the following pairs of points. Leave your answer insurd form if necessary.

a A(2, 1), B(5, 5) b A(3, 7), B(9, 15)

______________________________________ ______________________________________

______________________________________ ______________________________________

c A(–2, –5), B(4, –7) d A(–2, 3), B(2, –5)

______________________________________ ______________________________________

______________________________________ ______________________________________

e A(3, 4), B(6, 8) f A(6, –3), B(8, –7)

______________________________________ ______________________________________

______________________________________ ______________________________________

QUESTION 2 Calculate the length of each side of ∆ABC and by using Pythagoras’ Theorem findwhether or not it is a right angled triangle.

a A(0, 0), B(3, 0), C(3, 4) b A(1, 6), B(3, 2), C(–4, 3)

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

QUESTION 3a Find the distance between the points

A(–1, 3) and B(3, 8) and then square it.

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

b Find the perimeter of the triangle whosevertices are A(4, 0), B(7, 4) and C(–1, –2).

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

2

Coordinate geometry


48 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Coordinate geometryUNIT 2: The mid-point of an interval


Page 79

QUESTION 1 Find the mid-point of the interval joining the following points.

a (0, 4) and (0, 8) b (1, 5) and (3, 7)

______________________________________ ______________________________________

______________________________________ ______________________________________

c (–1, 4) and (–3, –2) d (2, 7) and (6, 1)

______________________________________ ______________________________________

______________________________________ ______________________________________

e (5, 0) and (3, 0) f (–2, 6) and (2, 2)

______________________________________ ______________________________________

______________________________________ ______________________________________

g (–1, –8) and (5, 2) h (7, 1) and (5, 3)

______________________________________ ______________________________________

______________________________________ ______________________________________

i (0, 8) and (6, 6) j (3, 4) and (5, 8)

______________________________________ ______________________________________

______________________________________ ______________________________________

k (–2, –5) and (2, 5) l (–6, 4) and (6, –4)

______________________________________ ______________________________________

______________________________________ ______________________________________

QUESTION 2 The vertices of a triangle ABC are A(–2, 5), B(6, 7) and C(3, –3). Find the mid-point ofeach side.

____________________________________________________________________________

____________________________________________________________________________

____________________________________________________________________________

QUESTION 3 The vertices of ∆PQR are P(2, 3), Q(10, 9) and R(8, 0).

a Find the mid-points of PR and QR. b Find the length of the interval joiningthese mid-points.

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

______________________________________ ______________________________________

Topic 2 - The mid-point of an interval

3

Coordinate geometry



Coordinate geometryUNIT 3: Different forms of linear equations


Pages 82–84

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

a 2 3 7x y+ = b x y− = −9 c 3 6 2x y− =

______________________ ______________________ ______________________

d 8 5 3y x+ = e 5 8x y− = f y x= −2 1

______________________ ______________________ ______________________

g y x= − +4 10 h 8 7 5x y− = i 3 4x y− = −

______________________ ______________________ ______________________

j yx= +3

1 k y x− = 14 l 9 8 3x y= −

______________________ ______________________ ______________________

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

a 3 6 12y x= + b 5 2 7y x= − + c 9 6+ =y x

______________________ ______________________ ______________________

d 8 3 9y x− = e y x+ =3 0 f 7 14x y− =

______________________ ______________________ ______________________

g x y+ = 1 h 3 8x y− = i 3 9 18y x= −

______________________ ______________________ ______________________

j y x+ =2 7 k 7 8 10y x= − l − =3 9y x

______________________ ______________________ ______________________

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

a y x= +2 1 ______________________________ b y x= −7 3 _____________________________

c y x= + 5 _______________________________ d y x= − +2 3 ____________________________

e y x= −1

22 _____________________________ f y x= −1

41 _____________________________

g y x= − −1

24______________________________ h y x= − ________________________________

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 b= =2 1, ____________ b m b= = −7 2, ___________ c m b= − =1 4, ___________

d m b= =1

23, ____________ e m b= − =4

33, ___________ f m b= − =2 9, ___________

Topic 3 - Different forms of linear equations

4

Coordinate geometry



Coordinate geometryUNIT 4: Graphing straight lines


Pages 84, 86

QUESTION 1 Complete the table of values and then draw the graph of each straight line.

a y x

x

y

= +1

0 1 2

b y x

x

y

= −2 1

0 1 2

c y x

x

y

= +4 3

0 1 2

d 2 3 6

0 1 2

x y

x

y

+ =

e y x

x

y

= −1

24

0 1 2

f y x

x

y

= − + 2

0 1 2

QUESTION 2 Find the x-intercept and y-intercept of the graphs of the following equations and thendraw the graph.

a y x

x

y

= +2 1

0

0

b y x

x

y

= + 2

0

0

c y x

x

y

= −3 2

0

0

d x y

x

y

+ = 3

0

0

QUESTION 3 On the same number plane draw the graphs of the following.

a y = 3x

b y = 3x + 2

c y = 3x – 1

What do you notice? __________________________________________________

QUESTION 4 Which of the following points lie on the line y = 2x + 1?

(0, 0), (1, 2), (0, 1), (1, 3), (–2, 1), (–2, –3) __________________________________________

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

0

y

x

Topic 4 - Graphing straight lines

5

Coordinate geometry



Coordinate geometryUNIT 5: The gradient of a straight line


Pages 79–80

QUESTION 1 Use the gradient formula my yx x

2 1

2 1= −

− to find the gradient of the straight line passing

through the following points.

a (1, 5) and (2, –7) b (–1, –2) and (3, 4) c (–2, –3) and (4, –7)

______________________ ______________________ ______________________

______________________ ______________________ ______________________

d (2, 4) and (–1, 3) e (5, 4) and (–1, 5) f (6, –2) and (8, –3)

______________________ ______________________ ______________________

______________________ ______________________ ______________________

g (–3, 6) and (–5, –1) h (8, 10) and (5, 1) i (3, 4) and (8, 6)

______________________ ______________________ ______________________

______________________ ______________________ ______________________

j (8, 1) and (4, 5) k (–3, 6) and (2, 4) l (0, 0) and (6, 9)

______________________ ______________________ ______________________

______________________ ______________________ ______________________

QUESTION 2 Show that (1, –1), (–1, 5) and (3, –7) are collinear.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

QUESTION 3 Which of the following sets of points are collinear?

a (1, 5), (–2, 3), (4, –2) b (0, 9), (4, 7), (6, 6) c (–2, –3), (0, 1), (–1, –1)

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

QUESTION 4 Show that the four points A(2, 6), B(5, 2), C(1, –1) and D(–2, 3) are the vertices of aparallelogram.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Topic 5 - The gradient of a straight line

6

Coordinate geometry



Coordinate geometryUNIT 6: Using the point-gradient formula to find the equation of a line


4

QUESTION 1 Find the general form of the equation of a line if it passes through:

a the point (3, 4) and has gradient 2. b the point (1, 3) and has gradient –1.

______________________________________ ______________________________________

______________________________________ ______________________________________

c the origin and has gradient 2. d the point (1, 5) and has gradient –2.

______________________________________ ______________________________________

______________________________________ ______________________________________

e the point (2, 5) and has gradient 1. f the point (1, 4) and has gradient 4.

______________________________________ ______________________________________

______________________________________ ______________________________________

g the point (–2, 7) and has gradient 1

2. h the point (2, 1) and has gradient

1

4.

______________________________________ ______________________________________

______________________________________ ______________________________________

i the point (3, 6) and has gradient 4. j the point (3, 3) and has gradient 2.

______________________________________ ______________________________________

______________________________________ ______________________________________

k the point (–5, 5) and has gradient –2. l the point (1, –2) and has gradient 3.

______________________________________ ______________________________________

______________________________________ ______________________________________

QUESTION 2 Find the equation of a straight line that passes through the point (2, –3) and has agradient of 2.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

QUESTION 3 Find the equation of a straight line that has a gradient of 3 and passes through themid-point of the interval joining the points (3, 5) and (7, 7).

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Topic 6 - Using the point–gradient formula to find the equation of a line

7

Coordinate geometry



Coordinate geometryUNIT 7: Using the two-point formula to find the equation of a line


Page 85

QUESTION 1 Find the general form of the equation of a line if it passes through the points:

a (1, 2) and (3, 4) b (1, 3) and (2, 5)

______________________________________ ______________________________________

______________________________________ ______________________________________

c (–1, 2) and (–3, –5) d (–2, 4) and (3, 4)

______________________________________ ______________________________________

______________________________________ ______________________________________

e (0, 0) and (5, 8) f (2, 2) and (5, 5)

______________________________________ ______________________________________

______________________________________ ______________________________________

g (1, 4) and (5, 6) h (0, –2) and (–1, –6)

______________________________________ ______________________________________

______________________________________ ______________________________________

i (3, 4) and (5, 6) j (7, 2) and (3, 4)

______________________________________ ______________________________________

______________________________________ ______________________________________

k (3, 1) and (1, 7) l (6, 3) and (4, 2)

______________________________________ ______________________________________

______________________________________ ______________________________________

QUESTION 2 Find the equation of the line that passes through the points (1, 5) and (2, 7). Show bysubstitution that the point (0, 3) lies on this line.

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

QUESTION 3 Find the equation of the straight line that passes through the points (0, 0) and (2p, 3p).

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

___________________________________________________________________________________________

Topic 7 - Using the two-point formula to find the equation of a line

8

Coordinate geometry



Coordinate geometryUNIT 8: Parallel and perpendicular lines


Page 87

QUESTION 1 State whether the following pairs of lines are parallel or not.

a x y x y+ + = + − =3 9 0 3 7 0and _________ b 2 6 3 7 9x y x y+ = − =and _________

c 3 7 8 0 3 7 2x y x y− + = − =and _________ d x y x y+ = + − =2 6 2 5 0and _________

e x y x y+ − = + − =2 0 7 0and _________ f y x y x= + = −4 3 4 5and _________

g y x y x= + = +2 1 2 8and _________ h y x y x= − = − +3 1 5 7and _________

QUESTION 4 Find the general form of the equation of the straight line passing through:

a the point (2, 5) and parallel to the line 3x – y + 7 = 0. ________________________________________

______________________________________________________________________________________

b the origin and parallel to the line 4x – 5y + 6 = 0. ___________________________________________

______________________________________________________________________________________

c the point (–2, 3) and perpendicular to the line 2x + y = 9. ____________________________________

______________________________________________________________________________________

d the point (3, –4) and perpendicular to the line x – y + 5 = 0. __________________________________

______________________________________________________________________________________

QUESTION 2 State whether the following pairs of lines are perpendicular or not.

a x y x y− = − − =3 7 3 2 0and _________ b 5 3 7 0 3 5 6 0x y x y− + = + − =and _________

c 2 7 8 3 4 7 0x y x y+ = − + =and _________ d 8 3 2 3 8 9x y x y− = + =and _________

e 5 6 15 6 5 3 0x y x y− = − + =and _________ f 2 3 7 0 3 2 5 0x y x y− + = + + =and _________

g 2 9 7 3 6 8x y x y− = + =and _________ h x y x y− = + =2 6 2 7and _________

QUESTION 3 State whether the following pairs of lines are parallel, perpendicular or neither.

a x y x y− + = − − =2 5 0 2 4 8 0and _________ b 3 3 0 9 3 1 0x y x y− − = − + =and _________

c x y x y+ = − =7 0 2 9 0and _________ d x y x y+ − = − + =7 0 3 3 3 0and _________

e 3 4 2 0 8 6 3 0x y x y− + = + − =and _________ f 4 8 8 2 9 6x y x y− = + =and _________

g x y x y+ − = + − =3 2 0 2 6 5 0and _________ h x y x y− − = + + =5 2 0 10 2 3 0and _________

QUESTION 5 Show that the lines x y x y− + = + − =2 7 0 and 2 16 0 are perpendicular to each other.

___________________________________________________________________________________________

___________________________________________________________________________________________

Topic 8 - Parallel and perpendicular lines


Coordinate geometryTOPIC TEST SECTION 1

Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question

1 The point (3, 6) lies on the line:

A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0

2 What is the gradient of the line that passes through the points (–2, 0) and (0, 4)?

A 1

2B 2 C − 1

2D –2

3 What is the slope of the line PQ?

A a

bB b

aC − a

bD − b

a

4 Find the length of the interval AB joining the points A(4, 2) and B(10, 10).

A 5 B 10 C 6 D 8

5 What is the equation of the line parallel to the x-axis passing through P(2, 4)?

A x = 4 B y = 2 C x = 2 D y = 4

6 The graph 3x + y = 9 cuts the x-axis at the point:

A (3, 0) B (0, 3) C (0, 9) D (9, 0)

7 What is the equation of the line which passes through the point (–2, 3) and has agradient of –2?

A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7

8 Which one of the following is a linear equation?

A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3

9 The mid-point of the interval joining the points (3, 7) and (–5, 3) is:

A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)

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

A 3

5B 5

3C 3 D –5

Marks

Total marks achieved for SECTION 110

1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry

9Coordinate geometryMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Coordinate geometryTopic Test PART A

Marks

Total marks achieved for PART A 10

Instructions This part consists of 10 multiple-choice questions Each question is worth 1 mark Attempt ALL questions Calculators are NOT to be used Fill in only ONE CIRCLE for each question

Time allowed: 15 minutes Total marks = 10

Total marks achieved for PART B 15

Marks

Coordinate geometryTopic Test PART B

10Coordinate geometryMathletics Instant Workbooks – Series J 2 Copyright © 3P Learning

Instructions This part consists of 15 questions Each question is worth 1 mark Attempt ALL questions Calculators may be usedTime allowed: 20 minutes Total marks = 15

Questions Answers only



Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used

Marks


The interval AB is between the points (–3, 2) and (6, 2) on anumber plane. Find:

1 the mid-point of AB. ___________________

2 the length of AB. ___________________

3 the gradient of AB. ___________________

The equation of a line is 2x – y – 3 = 0:

4 Make y the subject of this equation. ___________________

5 What is the gradient of this line? ___________________

6 What is the y-intercept of this line? ___________________

7 Is this line parallel to the line y = 2x + 1? ___________________

From the diagram opposite:

8 Find the mid-point of AC. ___________________

9 What is the length of AC? ___________________

10 Show that ∆ABC is isosceles. ___________________

11 Show that ∆ABC is a right angled triangle. ___________________

12 Find the mid-point M of AB. ___________________

13 Find the gradient of OM. ___________________

14 Show that the line which passes through themid-points of AC and AB is parallel to BC. ___________________

15 Change the equation y = 3x – 1 to the general form. ___________________

Questions Answers

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

0

y

x

3

2

1

321

–3

–2

–1

A(0, 3)

B

C(0, –3)

Coordinate geometry



Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used

Marks


The interval AB is between the points (–3, 2) and (6, 2) on anumber plane. Find:

1 the mid-point of AB. ___________________

2 the length of AB. ___________________

3 the gradient of AB. ___________________

The equation of a line is 2x – y – 3 = 0:

4 Make y the subject of this equation. ___________________

5 What is the gradient of this line? ___________________

6 What is the y-intercept of this line? ___________________

7 Is this line parallel to the line y = 2x + 1? ___________________

From the diagram opposite:

8 Find the mid-point of AC. ___________________

9 What is the length of AC? ___________________

10 Show that ∆ABC is isosceles. ___________________

11 Show that ∆ABC is a right angled triangle. ___________________

12 Find the mid-point M of AB. ___________________

13 Find the gradient of OM. ___________________

14 Show that the line which passes through themid-points of AC and AB is parallel to BC. ___________________

15 Change the equation y = 3x – 1 to the general form. ___________________

Questions Answers

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

0

y

x

3

2

1

321

–3

–2

–1

A(0, 3)

B

C(0, –3)

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry





A x + 2y + 12 = 0 B x + 2y – 12 = 0 C 2x + y + 12 = 0 D 2x + y – 12 = 0


A 1

2B 2 C − 1

2D –2


A a

bB b

aC − a

bD − b

a


A 5 B 10 C 6 D 8


A x = 4 B y = 2 C x = 2 D y = 4


A (3, 0) B (0, 3) C (0, 9) D (9, 0)


A y = 2x – 1 B y = –2x – 1 C y = 2x – 7 D y = 2x + 7


A y x= +2 7 B yx

= −57

C y x= −6 7 D y x= − 3


A (5, –1) B (–1, 5) C (–5, 1) D (–5, –1)


A 3

5B 5

3C 3 D –5

Marks


1

1

1

1

1

1

1

1

1

1

a

b

P

Q

Coordinate geometry

coordinate geometry - intranet.cesc.vic.edu.au · question 1 calculate the distance between the...

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