# Enlargement

**Enlargement**

**Enlargement** is when a shape is larger by a corresponding length to the original shape by a specific scale factor.

For example, if the length of a shape is 2x the length of the original shape, it has an enlarged **scale factor** of 2. Note: scale factors can also be written as decimals and fractions.

**Congruence and similarity**

When provided with an enlarged shape, corresponding angles are the same as the original but the length differ. The object and its image are called **similar**.

**The centre of enlargement**

Two factors are required when defining an enlargement, a **scale factor** and a **centre of enlargement**.

In the example below, the triangle ABC is enlarged by a scale factor of 2 from the centre of enlargement O.

Note: the distance from O to A’ is double from O to A.

**Negative scale factors**

A negative scale factor is when an enlargement is on the opposite side from the centre of enlargement. For example, the image below shows shape ABCD enlarged by a scale factor of -2 through the centre of enlargement O.

**Inverse enlargements**

An **inverse enlargement** is when an image has been enlarged back onto the original object. The general rule is that the inverse of an enlargement with a scale factor *k* is represented with a scale factor from the same centre of enlargement.

**Finding the centre of enlargement**

The centre of enlargement can be found using the following methods:

- lines should be draw from any two vertices to the image
- Extend lines until they are met at a certain point (see example below)