# How to Enlarge a Shape with a Fractional Scale Factor

## 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 center of enlargement (1, 1).

### Step-by-Step:

# 1

Plot the center of enlargement.

In our example, the Cartesian coordinates of the center 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 center 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 center 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 × ^{1}⁄_{3}

Scaled distance = 1 diagonal unit

The distance to the transformed point is 1 diagonal unit (or 1 unit across and 1 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**.

### 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 center of enlargement.