# How to Enlarge a Shape with a Negative Scale Factor

## 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 center 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 center of enlargement (5, 5).

### Step-by-Step:

# 1

Plot the center of enlargement.

In our example, the Cartesian coordinates of the center of enlargement is **(5, 5)**. It is 5 units along the x-axis and 5 units up the y-axis.

Each point on the shape is enlarged by the same amount.

Let us choose a point on the shape and transform it. We will transform point **A**.

# 2

Draw a line from point **A** to the center of enlargement.

**Note:** It is useful to extend the line beyond the center of enlargement.

# 3

Measure the length of the line from the point to the center of enlargement.

In our example, the point is 1 diagonal unit from the center of enlargement (or 1 unit across and 1 up).

# 4

Multiply this distance (2) by the scale factor. *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

The distance to the transformed point is 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 center 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 center of enlargement going away from the shape.

This is the point on the enlarged shape, which we will call **A'**.

We have transformed point **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 center of enlargement. It is also the other side of the center of enlargement and turned upside down.