# Dilation

A
**
dilation (similarity transformation)
**
is a transformation that changes the size of a figure. It requires a center point and a
scale factor
,
$k$
. The value of
$k$
determines whether the dilation is an enlargement or a reduction.

If $\left|k\right|>1$ , the dilation is an enlargement.

If $\left|k\right|<1$ , the dilation is a reduction.

The absolute value of the scale factor determines the size of the new image as compared to the size of the original image. When $k$ is positive the new image and the original image are on the same side of the center. When $k$ is negative they are on opposite sides of the center. The center of a dilation is always its own image.

Dilations preserve angle measure, betweenness of points and collinearity. It does not preserve distance. Simply, dilations always produce similar figures .