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.
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.