Scale factors transform the size of an original shape, diagram, or object, while keeping the relative proportions of that shape, diagram, or object consistent. The value of the scale factor tells whether the resulting representation will be larger or smaller than the original shape, diagram, or object.

Examine the following diagrams with their scale factors.

An enlargement occurs when the scale factor is .

Multiply the dimensions of the original by the scale factor to determine the dimensions of the representation.

12 cm × 2 = 24 cm

Or, use the scale factor formula.

A reduction occurs when the scale factor is .

Multiply the dimensions of the original by the scale factor to determine the dimensions of the representation.

Or, use the scale factor formula.

For further information about scale factors see p. 467 to 470 of Principles of Mathematics 11.