Positive or negative number that characterizes a dilation.

The scale factor is the ratio between an algebraic measure of the image figure and the corresponding algebraic measure on the initial figure.

In this illustration, \(k = \dfrac{\textrm{m}\textrm{(O, P}^{\prime})}{\textrm{m}\textrm{(O, P)}}\) = −\(\dfrac{\textrm{m}\textrm{(O, P}^{\prime\prime})}{\textrm{m}\textrm{(O, P)}}\).

### Properties

- If a scale factor k applies a figure F on a figure F’, then the ratio of similarity of F to F’ is given by \(\left| {\dfrac{1}{k}} \right|\).
- A negative dilation with centre C and scale factor
*k*can be expressed as the composition of a positive dilation with scale factor −*k*from centre C and a rotation of 180° around centre C.