Fractional Scale Factors

# Fractional Scale Factors

GCSE(F), GCSE(H),

Enlargements with a scale factor greater than 1 will always cause the shape to enlarge. If the scale factor is equal to 1, then the enlarged shape will be the same size in the same place. If the scale factor is zero, then the shape will effectively disappear.

If the scale factor is greater than zero, and less than 1, then the enlarged shape will be smaller than the original shape.

In the diagram below, Shape X has been enlarged with a scale factor of 0.5 with a centre of enlargement at (-8, -2) and mapped onto shape Y. The linear dimensions of the shape (the edges) will be half the size of the original. The distance AB will be half the value of the distance AC.

## Examples

1. A shape X is enlarged with a scale factor of frac(1)(2) with a centre of enlargement (-8, 2). Draw the enlarged shape on the graph.

Answer: Enlargement, centre of enlargement (-4, 7), scale factor frac(1)(3)
Draw ray lines from Shape X through Shape Y at each vertex. The ray lines will cross at (-4, 7). The size of the enlarged shape is frac(1)(3) the size of the original shape; a scale factor of frac(1)(3).