Centre of enlargement

The position of the enlarged shape is described by the centre of enlargement (O in the following diagrams).

Centre of enlargement diagram

Example

To enlarge the triangle with a scale factor of {2} and centre of enlargement O, take the following steps:

Centre of enlargement

Enlarging a triangle with a scale factor of 2

A line is drawn from the point O through point A of the triangle.

For a scale factor of {2}:

OA' = {2} × OA

OB' = {2} × OB

OC' = {2} × OC

For a scale factor of {3}:

OA' = {3} × OA

OB' = {3} × OB

OC' = {3} × OC

Sometimes the centre of enlargement lies on or within the original shape. Look at the following examples:

Question

What are the scale factors of enlargement for shapes A and B?

Scale factor of enlargement diagram

A) {2}

B) {3}