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Scale Factor
(KS3, Year 7)
The Lesson
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 k^{2} times the area of the object.

The volume of the image will be k^{3} times the volume of the object.
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