## 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.