Enlargements

An enlargement is a transformation that changes the size of a shape but keeps its proportions the same. The shape becomes either larger or smaller depending on the scale factor. When using a positive scale factor, the shape gets either bigger (for scale factors greater than 1) or smaller (for scale factors between 0 and 1), but the shape itself remains the same shape (i.e., it is not distorted).

Key Concepts

• Centre of Enlargement: The point from which the shape is enlarged. The shape is enlarged in such a way that every point moves along a straight line passing through this centre.
• Scale Factor: The ratio by which the shape is enlarged. A scale factor greater than 1 makes the shape larger, and a scale factor between 0 and 1 makes it smaller. A scale factor of 1 keeps the shape the same size.

How to Perform an Enlargement

1. Identify the centre of enlargement. This is the point from which all points of the shape will be enlarged. It may be given in the problem or chosen arbitrarily.
2. Determine the scale factor. If the scale factor is greater than 1, the shape becomes larger. If the scale factor is between 0 and 1, the shape becomes smaller.
3. For each point on the shape, draw a line from the centre of enlargement to the point.
4. Measure the distance from the centre of enlargement to the point. Multiply this distance by the scale factor to find the new distance.
5. Move the point along the line in the same direction from the centre. Place the new point at the calculated distance.
6. Repeat the process for all points of the shape to find the enlarged shape.