Dilation and Scale Factor
Concept

Dilation

A dilation is a transformation that changes the size of a figure while keeping its shape the same. This transformation involves enlarging or reducing the figure by a certain length scale factor k from a fixed point O called the center of dilation. For example, the image of every point on a leaf lies on the ray that starts at the center of the dilation and passes through its preimage.
As shown in the diagram, O is the center of the dilation, k is the scale factor, A is the preimage, and A' is the image point. By definition, the scale factor k can also be defined as the ratio of a length in the image to the corresponding length in the preimage.


OA'=k * OA ⇔ k = OA'/OA

When the scale factor is greater than 1, the dilation is called an enlargement because the image is larger than the preimage. When the scale factor is between 0 and 1, the dilation is called a reduction because the image is smaller than the preimage.

Exercises