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.