Describing an Enlargement
(KS3, Year 7)

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).
We have found the centre of enlargement. We can find the scale factor.

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.

Answer:

The shape has been enlarged about the centre of enlargement (1, 0) by a scale factor of 2.

Lesson Slides

The slider below shows another real example of how to describe an enlargement. Open the slider in a new tab

What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.
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See Also

What is geometry? What are transformations? What are Cartesian coordinates?