is a that changes a figure in a particular way — it can change the position, size, and orientation of a figure. The original figure is called the preimage
and the produced figure is called the image
of the transformation. To denote the image of a labeled point, a prime symbol is added next to the previous label.
Transformations are sometimes expressed as a mapping. That is, it maps the to the . Note that the input can be a single point.
Here, is the transformation, are the coordinates of the points of the preimage, and are the coordinates of the points of the image.