## Enlarging a Shape

A shape can be enlarged. It can be made larger or smaller.

## How to Enlarge a Shape

Enlarging a shape is easy.

## Question

Enlarge the shape below by a scale factor of 3 about the centre of enlargement (1, 1). # 1

Plot the centre of enlargement. In our example, the Cartesian coordinates of the centre of enlargement is (1, 1). It is 1 unit along the x-axis and 1 unit 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 the centre of enlargement to point A. Note: It is useful to extend the line beyond the point.

# 3

Measure the length of this line. 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 (1) by the scale factor (3).

Scaled distance = Distance × Scale factor

Scaled distance = 1 diagonal unit × 3

Scaled distance = 3 diagonal units

The distance to the transformed point is 3 diagonal units (or 3 units across and 3 up).

# 5

Measure the distance found in Step 4 along the line drawn in Step 2. 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.  By multiplying the shape by a scale factor of 3, the enlarged shape is 3 times larger and 3 times the distance from the centre of enlargement.