# Scale Factor(KS3, Year 7)

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A scale factor is used to describe an enlargement. A scale factor describes how much larger (or smaller) the enlarged shape is compared to the original shape.

## Dictionary Definition

The Oxford English Dictionary defines a scale factor as "a numerical factor by which each of a set of quantities is multiplied."

## Understanding a Scale Factor

When a shape is enlarged, the length of each side becomes larger (or smaller). Each side becomes larger (or smaller) by same amount. The length of each side is multiplied by a scale factor.

## A Real Example of a Scale Factor

A scale factor is easier to understand with an example. The image below shows a light blue shape being enlarged to a dark blue shape.The scale factor is 2. Each side of the dark blue shape is 2 × longer than the corresponding side of the light blue shape.

## Types of Scale Factors

Scale factors have different effects depending on how large the number is.
Scale Factor Description
Greater than 1 The shape gets larger
Equal to 1 The shape stays the same size
Greater than 0, less than 1 The shape gets smaller
Negative The shape is on the other side of the center of enlargement, and is the other way around

## What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.

## Scaling Lengths, Areas and Volumes

If a scale factor is k:
• Each length on the image will be k times the length of the object.
• The area of the image will be k2 times the area of the object.
• The volume of the image will be k3 times the volume of the object.

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