## The Lesson

A shape can be enlarged. To describe an enlargement, we need to describe the centre of enlargement and the scale factor.## The Centre of Enlargement

The centre of enlargement is the point about which a shape is enlarged.The centre of enlargement can be described using Cartesian coordinates.## The Scale Factor

The scale factor describes how much larger (or smaller) the enlarged shape is compared to the original shape.The scale factor is found by dividing a length of a side of the enlarged shape to the length of the corresponding side of the original shape.## How to Describe an Enlargement

Describing an enlargement is easy.## Question

Describe the enlargement of the light blue shape to the dark blue shape below.## Step-by-Step:

# 1

Find a point on the shape and the corresponding point on the enlarged shape.We will choose point

**A**on the shape. Point**A'**is the corresponding point on the enlarged shape.# 2

Join the pair of corresponding points with a line.

# 3

Find another point on the shape and the corresponding point on the enlarged shape.We will choose point

**B**on the shape. Point**B'**is the corresponding point on the enlarged shape.# 4

Join the pair of corresponding points with a line.

# 5

Draw the centre of enlargement where the two lines meet.

# 6

Describe the centre of enlargement in Cartesian coordinates.
In our example, the Cartesian coordinates of the centre of enlargement is

**(1, 0)**.# 7

Find the length of a side on the enlarged shape.
The length of the side

**A'B'**is**4**.# 8

Find the length of the corresponding side on the original shape.
The length of the side

**AB**is**2**.# 9

Divide the length on the enlarged shape (4) by the length on the original shape (2).
The scale factor is

$$Scale factor = \frac{A'B'}{AB}$$

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = \frac{4}{2}$$

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 2$$

**2**.## Answer:

The shape has been enlarged about the centre of enlargement**(1, 0)**by a scale factor of

**2**.