## 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**.

## What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.## You might also like...

transformationsenlarging a shape with a negative scale factordescribing an enlargement with a negative scale factorgraphs and coordinates curriculum

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.

## Worksheet

This test is printable and sendable