## 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 (
The distance to the transformed point is 1 diagonal unit (or 1 unit across and 1 up).

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

Scaled distance = 3 diagonal units × ^{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.

## You might also like...

transformationsenlarging a shapeenlarging a shape with a negative scale factordescribing an enlargement

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.

next up:

## What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.## Why Do Fractional Scale Factors Shrink a Shape?

A scale factor multiplies the length of each side of the shape that is enlarged. If a scale factor is a fraction between 0 and 1, then each side is going to get smaller. For example, multiplying a length by^{1}⁄

_{2}will make each side half as long as it was before - which is shorter.

## Fractional, Negative Scale Factors

A scale factor can be a fraction and negative. For example, a scale factor of −^{1}⁄

_{2}will also shrink a shape.The shape is smaller (because of the fraction) but also on the other side of the center of enlargement and turned upside down (because of the − sign).