# Enlargement

## Enlargement

When two figures F and F’ are similar, F’ is said to be an enlargement of F if the scale factor r of F’ to F is greater than 1.

An enlargement is the result of a dilation, for which the absolute value of the scale factor r is strictly greater than 1.

### Example

Consider the similar triangles ABC and A’B’C’:

The ratio of their corresponding side lengths, the scale factor r = 2.

Triangle A’B’C’ is an enlargement of triangle ABC.

$$\dfrac{\textrm{m}\space \overline{\textrm{A′C′}}}{\textrm{m}\space \overline{\textrm{AC}}}=\dfrac{\textrm{m}\space \overline{\textrm{B′C′}}}{\textrm{m}\space \overline{\textrm{BC}}}=\dfrac{\textrm{m}\space \overline{\textrm{A′B′}}}{\textrm{m}\space \overline{\textrm{AB}}}=2$$

It can be stated that triangle ABC is a reduction of triangle A’B’C’. In this case, the scale factor r of triangle ABC to triangle A’B’C’ is 0.5.

$$\dfrac{\textrm{m}\space \overline{\textrm{AC}}}{\textrm{m}\space \overline{\textrm{A′C′}}}=\dfrac{\textrm{m}\space \overline{\textrm{BC}}}{\textrm{m}\space \overline{\textrm{B′C′}}}=\dfrac{\textrm{m}\space \overline{\textrm{AB}}}{\textrm{m}\space \overline{\textrm{A′B′}}}=0.5$$