Enlargement

# Enlargement

GCSE(F), GCSE(H),

An Enlargement is the only transformation that changes the size of a shape. Two items of information are needed to enlarge a shape: the Centre of Enlargement and the Scale Factor.

Locate the Centre of Enlargement, then draw Ray Lines from the centre of enlargement through the vertices of the shape. If a shape is being enlarged by a scale factor of 2, the distance from the centre of enlargement to each vertex will be twice the size. The size of the shape will also be twice the size.

## Examples

1. Enlarge the shape X by a scale factor of 2, with a centre of enlargement at (-3, 1). Answer: One vertex of the triangle is at (2, 2). This is 5 along from the centre of enlargement; and 1 up. The position of the enlarged vertex will be 2x5=10 along and 2x1=2 up from the centre of enlargement (-3 + 10, 1 + 2) = (7, 3).

Similarly, draw the other two vertices. Check that the shape is now twice the size: shape has gone from being 2 tall and 1 wide, to 4 tall and 2 wide.

2. Shape X is mapped onto shape Y. What is the transformation? Answer: Enlargement, scale factor 3, centre of enlargement (-8, 9)

Check the lengths of the sides: each side is 3x larger, so it is a scale factor of 3. Draw ray lines from each pair of vertices on the two shapes to intersect at (-8, 9). this is the centre of enlargement. 