## Enlarging a Shape with a Negative Scale Factor

A shape can be enlarged with a negative scale factor. If the scale factor is negative, the shape is enlarged on the other side of the centre of enlargement and it is turned upside down.## How to Enlarge a Shape with a Negative Scale Factor

Enlarging a shape with a negative scale factor is easy.## Question

Enlarge the shape below by a scale factor of −2 about the centre of enlargement (5, 5).## Step-by-Step:

## 1

Plot the centre of enlargement.
In our example, the Cartesian coordinates of the centre of enlargement is

**(5, 5)**. It is 5 units along the x-axis and 5 units up the y-axis.**A**.

## 2

Draw a line from point

**A**to the centre of enlargement.**Note:**It is useful to extend the line beyond the centre of enlargement.## 3

Measure the length of the line from the point to the centre of enlargement.
In our example, the point is 1 diagonal unit from the centre of enlargement (or 1 unit across and 1 up).

## 4

Multiply this distance (2) by the scale factor.
The distance to the transformed point is 2 diagonal units.

*Ignore the − sign in front of the scale factor for now.*Scaled distance = Distance × Scale factor

Scaled distance = 1 diagonal units × 2

Scaled distance = 2 diagonal units

*Now we use the − sign in the scale factor.*Because the scale factor is negative, the distance will be on the other side of the centre of enlargement. The 2 diagonal units will be 2 units to the left and 2 units down.## 5

Measure the distance found in

**Step 4**along the line drawn in**Step 2**. Measure it from the centre of enlargement going away from the shape. This is the point on the enlarged shape, which we will call**A'**.**A**to point

**A'**on the enlarged shape. Repeat for points

**B**and

**C**.

## Answer:

With all the vertices (corners) of the shape transformed, the enlarged shape can be drawn:By multiplying the shape by a scale factor of −2, the enlarged shape is 2 times larger and 2 times the distance from the centre of enlargement. It is also the other side of the centre of enlargement and turned upside down.

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## What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.## Negative, Fractional Scale Factors

A scale factor can be negative and a fraction. For example, a scale factor of −^{1}⁄

_{2}will also enlarge a shape on the other side of the center of enlargement and turned upside down.The shape is on the other side of the center of enlargement and turned upside down (because of the − sign) but it is also smaller (because of the fraction).