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 Scale Factor
The scale factor describes how much larger (or smaller) the enlarged shape is compared to 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).
$$Scale factor = \frac{A'B'}{AB}$$
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = \frac{4}{2}$$
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 2$$
The scale factor is 2.