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.

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.