## Enlarging a Shape with a Fractional Scale Factor

A shape can be enlarged with a scale factor. Usually, this makes the shape larger. If the scale factor is a fraction (between 0 and 1), the enlargement makes the shape smaller.## How to Enlarge a Shape with a Fractional Scale Factor

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

Enlarge the shape below by a scale factor of^{1}⁄

_{3}about the centre of enlargement (1, 1).

## Step-by-Step:

# 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.**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 3 diagonal units from the centre of enlargement (or 3 units across and 3 up).

# 4

Multiply this distance (3) by the scale factor (

^{1}⁄_{3}).
Scaled distance = Distance × Scale factor
Scaled distance = 3 diagonal units ×

The distance to the transformed point is 1 diagonal unit (or 1 unit across and 1 up).
^{1}⁄_{3}Scaled distance = 1 diagonal unit# 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'**.**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

^{1}⁄

_{3}, the enlarged shape is a

^{1}⁄

_{3}of the size and a

^{1}⁄

_{3}the distance from the centre of enlargement.