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11.02 Directed numbers on the number plane

Worksheet
Directed numbers on the number plane
1

Consider the following number plane:

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
y

State the coordinates of the following points:

a
A
b
B
c
C
d
D
e
E
f
F
g
G
h
H
i
I
j
J
k
K
l
L
m
M
n
N
o
O
p
P
2

Consider the following number plane:

State the coordinates of the following points:

a
A
b
B
c
C
d
D
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
3
a

State the x-coordinate of:

i

The origin.

ii

Any point on the y-axis.

b

State the y-coordinate of:

i

The origin.

ii

Any point on the x-axis.

4

If point P has an x-coordinate of 0, which axis must it lie on?

5

If \left(a, b\right) is a point that lies on the y-axis, find the value of a.

6

Consider the given points on the number plane:

State which point has the following coordinates:

a

\left(9, - 3 \right)

b

\left( - 4 , - 7 \right)

c

\left(2, 4\right)

d

\left( - 8 , 8\right)

-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
7

Consider the points A and B plotted on the number plane:

a

Write down the coordinates of point A.

b

Write down the coordinates of point B.

c

Which axis do points A and B lie on?

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
8

In which quadrant do the following points lie?

a
\left(7, 8\right)
b
\left( - 3 , 4\right)
c
\left(2, - 1 \right)
d
\left( - 5 , - 6 \right)
9

State the quadrant(s) that have:

a

Points with a negative y-coordinate.

b

Points with a negative x-coordinate.

c

Points where the x-coordinate and y-coordinate have the same sign.

d

Points with a negative x-coordinate and a positive y-coordinate.

e

Points with a negative x-coordinate and a negative y-coordinate.

10

Plot the following points on a number plane:

a
A\left(6, 1\right)
b
B\left( - 7 , 3\right)
c
C\left(7, - 4 \right)
d
D\left( - 7 , - 3 \right)
e
E\left( - 4 , - 4 \right)
f
F\left( - 6 , 0\right)
g
G\left(2, 6\right)
h
H\left(2, - 8 \right)
i
I\left( - 6 , 3\right)
j
J\left( - 5 , - 5 \right)
k
K\left(- 5, 9 \right)
l
L\left(5, - 9 \right)
m
M\left( 3 , - 3 \right)
n
N\left( 0 , 8 \right)
o
O\left(1, 3\right)
p
P\left( - 4 , 5\right)
q
Q\left( - 2 , - 4 \right)
r
R \left(4, - 3 \right)
s
S\left(1, 0\right)
t
T\left(0, 2\right)
11

For each of the following points:

i

Plot the point on a number plane.

ii

State which quadrant the point lies in.

a

\left(2, 5\right)

b

\left( - 2 , 1\right)

c

\left(- 3 ,- 5 \right)

d

\left(8, - 5 \right)

e

\left( -8 ,- 1 \right)

f

\left( 4 ,- 7 \right)

g

\left(0, 2\right)

h

\left(5, 0\right)

12

For each of the following sets of points:

i

Plot the points on a number plane.

ii

Identify the shape formed by joining the points in order.

a

\left(4, 1\right), \left(7, 1\right), \left(4, 4\right), \left(7, 4\right)

b

\left(1, 5\right), \left(6, 5\right), \left(1, 8\right), \left(6, 8\right)

c

\left( - 5 , - 3 \right), \left(0, -1 \right), \left( - 4 , 6 \right), \left(1, 8 \right)

d

\left( - 4 , - 3 \right), \left(0, -1 \right), \left( - 2 , 1 \right), \left(2, 3 \right)

13

For each of the following shapes, write down the coordinates of the vertices:

a
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
b
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
c
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
d
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
14

Describe how you would move on the number plane from the origin, to plot the following points:

a
\left(2, - 4 \right)
b
\left(9, 14\right)
15

Find the coordinates of the following points given the description:

a

The point 9 units below the origin.

b

The point 3.5 units to the left of the origin.

c

The point 4 units to the left of \left( - 3 , 6 \right).

d

The point 7 units to the right of \left( - 1 , - 2 \right).

e

The point 2 units to the right and 2 units below the point \left(2, 5\right).

f

The point 6 units to the left and 5 units above the point \left(4, -4\right).

16

Which point is furthest from the origin?

A

\left(0, - 3 \right)

B

\left(5, 0\right)

C

\left(0, 4.5\right)

D

\left( - 4 , 0\right)

17

How many units above the origin is the point \left( - 6 , 1\right) located?

18

Starting at the origin, move 4 units left and then 4 units up.

a

Plot the resulting point on a number plane.

b

State the coordinates of this point.

Distance between two points
19

Find the distance between the following pairs of points:

a

A \left( - 5 , 8\right) and B \left( - 2 , 8\right).

b

A \left(7, 3\right) and B \left(-1, 3\right).

c

A \left(6, - 5 \right) and B \left(6, -1\right).

d

A \left( - 6 , 2\right) and B \left( - 6 , - 7 \right).

20

Consider the points: A \left( - 4 , 8\right), B \left( - 7 , 8\right) and C \left( - 7 , 1\right).

a

Plot the points on a number plane.

b

Find the length of AB.

c

Find the length of BC.

21

A triangle has points A \left(1, 2\right), B \left( - 2 , - 3 \right) and C \left(6, - 3 \right).

a

Plot the triangle ABC on a number plane.

b

Find the perpendicular height of the triangle if BC is the base.

c

Find the length of base BC.

d

Find the area of triangle ABC.

Geometric applications
22

The points given represent three vertices of a parallelogram. Find the coordinates of the fourth vertex if it is known to be in the 2nd quadrant.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
23

The points given represent three vertices of a rhombus. Find the coordinates of the fourth vertex if the missing point lies in the 3rd quadrant.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
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