# How to Describe an Enlargement

## Describing an Enlargement

A shape can be enlarged.

To describe an enlargement, we need to describe the center of enlargement and the scale factor.

### The Center of Enlargement

The center of enlargement is the point about which a shape is enlarged.

The center 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 center of enlargement where the two lines meet.

# 6

Describe the center of enlargement in Cartesian coordinates.

In our example, the Cartesian coordinates of the center of enlargement is **(1, 0)**.

We have found the center 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).

The scale factor is **2**.

### Answer:

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