Enlargement is when a shape is larger by a corresponding length to the original shape by a specific scale factor.
For example, if the length of a shape is 2x the length of the original shape, it has an enlarged scale factor of 2. Note: scale factors can also be written as decimals and fractions.
Congruence and similarity
When provided with an enlarged shape, corresponding angles are the same as the original but the length differ. The object and its image are called similar.
The centre of enlargement
Two factors are required when defining an enlargement, a scale factor and a centre of enlargement.
In the example below, the triangle ABC is enlarged by a scale factor of 2 from the centre of enlargement O.
Note: the distance from O to A’ is double from O to A.
Negative scale factors
A negative scale factor is when an enlargement is on the opposite side from the centre of enlargement. For example, the image below shows shape ABCD enlarged by a scale factor of -2 through the centre of enlargement O.
An inverse enlargement is when an image has been enlarged back onto the original object. The general rule is that the inverse of an enlargement with a scale factor k is represented with a scale factor from the same centre of enlargement.
Finding the centre of enlargement
The centre of enlargement can be found using the following methods:
- lines should be draw from any two vertices to the image
- Extend lines until they are met at a certain point (see example below)