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 $A^{\prime }$ 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.