Topics
2 Coordinate geometry
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Stage 5.1

2.03 The distance between two points

Lesson
Worksheet
Practice
Worksheet
Distance from a graph
1

Find the length of each vertical interval on the following number planes:

a

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

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

A \left(4, - 5 \right) and B \left(4, 5\right)

-4
-3
-2
-1
1
2
3
4
5
6
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
c

A \left(-7, -1\right) and B \left(-7, -6\right)

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

A \left( - 2 , 2\right) and B \left( - 2 , - 3 \right)

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

Find the length of each horizontal interval on the following number planes:

a

A \left(3, 2\right) and B \left(9, 2\right)

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

A \left( - 5 , - 4 \right) and B \left(9, - 4 \right)

-6
-4
-2
2
4
6
8
10
x
-6
-5
-4
-3
-2
-1
y
c

A \left( 3 , - 1 \right) and B \left(-5, - 1 \right)

-6
-5
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
y
d

A \left( - 4 , 5\right) and B \left( - 7 , 5\right)

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

Determine how far are the given points P from the origin. Round your answers to two decimal places if necessary.

a

P\left(12, 16\right)

2
4
6
8
10
12
14
16
x
2
4
6
8
10
12
14
16
y
b

P \left(7, 11\right)

1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
10
11
y
c

P \left( - 12 , 16\right)

-16
-14
-12
-10
-8
-6
-4
-2
x
2
4
6
8
10
12
14
16
y
d

P \left( - 3 , - 7 \right)

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

For each of the following right-angled triangles:

i

Find the length of interval PQ.

ii

Find the length of interval QR.

iii

Find the length of PR, rounding to two decimal places if necessary.

a

P \left( - 6 , 5\right), Q \left( - 6 , 2\right) and R \left( - 2 , 2\right)

-7
-6
-5
-4
-3
-2
-1
x
1
2
3
4
5
6
y
b

P \left( - 1 , 9\right), Q \left( - 1 , 6\right) and R \left( - 5 , 6\right)

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

P \left( - 4 , 6\right), Q \left( - 4 , 2\right) and R \left(3, 2\right)

-4
-3
-2
-1
1
2
3
4
x
-1
1
2
3
4
5
6
y
d

P \left( - 3 , - 6 \right), Q \left( - 3 , - 1 \right) and R \left(1, - 1 \right)

-4
-3
-2
-1
1
2
x
-6
-5
-4
-3
-2
-1
y
5

For each of the following right-angled triangles:

i

Find the length of interval AB.

ii

Find the length of interval BC.

iii

Find the length of AC, rounding to two decimal places if necessary.

a

A \left( - 2 , 4\right), B \left( - 2 , - 1 \right) and C \left( - 14 , - 1 \right)

-14
-12
-10
-8
-6
-4
-2
x
-2
-1
1
2
3
4
y
b

A \left( - 2 , 7\right), B \left( - 2 , - 4 \right) and C \left(5, - 4 \right)

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

For each of the following right-angled triangles, find the length of side AC. Round your answer to two decimal places if necessary.

a
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
y
b
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
y
7

For each of the following, find the length of interval AC, rounding your answer to two decimal places if necessary:

a
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
y
b
-2
-1
1
2
3
4
x
1
2
3
4
5
6
7
8
9
10
11
12
y
c
1
2
3
4
5
6
7
8
9
x
-3
-2
-1
1
2
3
4
5
6
y
d
-2
-1
1
2
3
4
5
6
7
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
e
-3
-2
-1
1
2
3
4
5
6
x
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
y
Distance from a pair of coordinates
8

Find the exact distance between Point A and Point B:

a

A \left(1, 4\right) and B \left(7, 12\right)

b

A \left(4, 2\right) and B \left( - 8 , - 7 \right)

c

A \left( - 1 , 9\right) and B \left( - 4 , 1\right)

d

A \left(-1, - \dfrac{3}{5} \right) and B \left(4, \dfrac{12}{5}\right)

9

Consider the points M \left( - 9 , - 1 \right) and N \left(1, 5\right).

a

Find the exact distance from M to the origin.

b

Find the exact distance from N to the origin.

c

Which point is closer to the origin?

10

Given P \left(4, 3\right), M \left( - 3 , - 4 \right) and N \left( - 7 , 1\right).

a

Find the distance from P to M to two decimal places.

b

Find the distance from P to N to two decimal places.

c

Which point is further from P?

11

Consider the Points A \left(12, 3\right) and B \left(14, 0\right).

a

Find the length of AB to two decimal places.

b

If M is the midpoint of AB, find the length of AM to two decimal places.

12

Consider the points A \left( - 2 , - 6 \right), B \left(4, - 2 \right) and C \left(1, - 4 \right). Find:

a

The exact distance AC.

b

The exact distance BC.

c

What do you notice about the distance between the points?

13

K is the midpoint of A \left(3, 1\right) and C \left(15, - 7 \right). Find the distance from A to K correct to one decimal place.

14

AB is a vertical interval 3 units long. If A is the point \left( - 2 , 6\right), find two possible coordinates of point B.

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MA5.1-6NA

determines the midpoint, gradient and length of an interval, and graphs linear relationships

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