Chap08

CH

AP

T ER

8

Coordinates

1. Label the x-axis, y-axis and the origin for the following.

3 2 1 0

2

4

6

8

2. Plot each of the following points on the Cartesian plane and state the coordinates in the table below. y 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

x

Point

Distance from y-axis

Distance from x-axis

(a)

Q

1

3

(b)

R

8

2

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Coordinates

3. Plot each of the following points on the Cartesian plane and state the distance of each point from the x-axis and y-axis in the table below. y 9 8 7 6 5 4 3 2 1 0

1

2

3

Point

Coordinates

(a)

Q

(8, 7)

(b)

S

(4, 1)

4

5

6

7

8

x

9

Distance from y-axis

Distance from x-axis

4. Based on the points on the Cartesian plane, state the coordinates in the table below. y 7 6 5 4 3 2 1 –5 –4 –3 –2 –1 0 –1 –2 –3

1

2

3

4

x

T

–4 S

–5 –6

Point (a)

S

(b)

T

Coordinates

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5. For the following Cartesian plane, mark the values on both axes by extending the sequence of the given values on the axes. y

1 0 –1

3

x

9 12

6

6. State the scales used for x-axis and y-axis in the following Cartesian plane. y 18 12 6 0

3

6

9

x

Scale : x-axis =

y-axis =

7. Mark the values on the axes with reference to the given scales. Scale: x-axis = 1 : 4 y-axis = 1 : 1 y

0

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40

x

8. State the coordinates of point Q on the following Cartesian plane with reference to the given scales. Scale : x-axis = 1 : 4 y-axis = 1 : 5 y

Q x

0

9. Plot each of the given points on the following Cartesian plane with reference to the given scales. Scale : x-axis = 1 : 2 y-axis = 1 : 1 P(2, 2), Q(6, –1) and R(–4, 5) y

x

0

10. By using a scale of 1 : 2 on the x-axis and a scale of 1 : 5 on the y-axis, plot the points P(–2, 20), Q(4, 10), R(0, –5) and S(–6, 5). State the shape formed. y

x

11. Find the distance between the points (–6, 5) and (8, 5).

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12. Find the distance between the points P and Q. P

Q

Distance of PQ

(a)

(6, –9)

(6, 4)

(b)

(12, 8)

(12, 1)

13. Find the distance of each of the following lines on the Cartesian plane. y M

5

Line

4 3 2

N

1 – 8 – 6 – 4– 2 0 2 –1 R –2

4

6

8 S

x

(a)

MN

(b)

RS

Distance

–3 –4 –5

14. Calculate the distance between the points (–5, 4) and (7, –1). 15. Find the length of the following lines. Give your answer correct to two decimal places. y Q

5

Line

4 3 2 1

–10 –8 –6 –4 –2 0 –1 –2 P

–3

Length

R

S 2

4

6

8 10 12

x

(a)

QR

(b)

RS

(c)

SP

–4

16. Given A(6, p), B(14, 22) and the distance of AB is 17 units. Find the values of p.

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42

17. Based on the points given on the Cartesian plane, complete the table below. y 4

Line

3 2 1 –3 –2 –1 0 V –1 –2 –3

1

2

3 4 S U

5

x

(a)

VU

(b)

ST

Midpoint

T

–4

18. Find the coordinates of the midpoint of the line joining points (5, 4) and (–3, –10). 19. Given a rhombus OPQR with O is the origin, P(4, 3) and R(3, 4). Find the coordinates of Q.

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