A dilation is a point transformation given by a center point O and a scale factor r.
The image of each point is on the ray starting at the center and going through the preimage. The distance of the image from the center is calculated as follows.
In this formula O is the center of the dilation, r is the scale factor, A is the preimage, and A′ is the image point. This is illustrated on the diagram. Move point A and see how the image point moves.
When the scale factor is greater than 1, the dilation is called an enlargement. When the scale factor is between 0 and 1, the dilation is called a reduction.