# Enlarging a Shape with a Fractional Scale Factor(KS3, Year 8)

homesitemaptransformationsenlarging 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 13 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 3 diagonal units from the centre of enlargement (or 3 units across and 3 up).

## 4

Multiply this distance (3) by the scale factor (13).

Scaled distance = Distance × Scale factor

Scaled distance = 3 diagonal units × 13

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.

With all the vertices (corners) of the shape transformed, the enlarged shape can be drawn:

By multiplying the shape by a scale factor of 13, the enlarged shape is a 13 of the size and a 13 the distance from the centre of enlargement.

## Lesson Slides

The slider below shows another real example of how to enlarge a shape with a fractional scale factor.

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## 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 12 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 −12 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).