# How to Describe an Enlargement with a Negative Scale Factor

## Describing an Enlargement with a Negative Scale Factor

A shape can be enlarged with a negative scale factor.

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.

When there is a negative scale factor, the center of enlargement is between the original shape and the enlarged shape.

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.

When there is a negative scale factor, the enlarged shape is turned upside down. Care needs to be taken when finding the corresponding lengths.

## How to Describe an Enlargement with a Negative Scale Factor

Describing an enlargement with a negative scale factor 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.

We will choose point **A** on the shape.

# 2

Find where the corresponding point on the enlarged shape will be.

When there is a negative scale factor, the enlarged shape looks like it has been turned upside down. In fact, the shape turned a half turn (rotated 180°).

Imagine turning the original shape a half turn.

The corresponding point will be at the bottom right corner of the triangle.

# 3

Draw the corresponding point on the enlarged shape.

The corresponding point is the bottom right corner of the triangle.

Point **A'** is the corresponding point on the enlarged shape.

# 4

Join the pair of corresponding points with a line.

# 5

Find another point on the shape.

We will choose point **B** on the shape.

# 6

Find where the corresponding point on the enlarged shape will be.

When there is a negative scale factor, the enlarged shape looks like it has been turned upside down. In fact, the shape turned a half turn (rotated 180°).

Imagine turning the original shape a half turn.

The corresponding point will be at the bottom left corner of the triangle.

# 7

Draw the corresponding point on the enlarged shape.

The corresponding point is the bottom left corner of the triangle.

Point **B'** is the corresponding point on the enlarged shape.

# 8

Join the pair of corresponding points with a line.

# 9

Draw the center of enlargement where the two lines meet.

# 10

Describe the center of enlargement in Cartesian coordinates.

In our example, the Cartesian coordinates of the center of enlargement is **(3, 2)**.

We have found the center of enlargement.

We can find the scale factor.

# 11

Find the length of a side on the enlarged shape.

The length of the side **A'B'** is **4**.

# 12

Find the length of the corresponding side on the original shape.

The length of the side **AB** is **2**.

# 13

Divide the length on the enlarged shape (4) by the length on the original shape (2).

# 14

Find the negative of this number (2) to find the scale factor.

### Answer:

The shape has been enlarged about the center of enlargement **(3, 2)** by a scale factor of **−2**.