A transformation is a function 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 inputs to the outputs. Note that the input can be a single point.
Here, T is the transformation, (x,y) are the coordinates of the points of the preimage, and (x′,y′) are the coordinates of the points of the image.