A transformation is a mathematical function that repositions points in a one-dimensional, two-dimensional, three-dimensional, or any other n-dimensional space. In this article, only transformations in the familiar twodimensional rectangular coordinate plane will be discussed.

Transformations map one set of points onto another set of points, generally with the purpose of changing the position, size, and/or shape of the figure made up by the first set of points. The first set of points, from the domain of the transformation, is called the set of pre-images, whereas the second set of points, from the range of the transformation, is called the set of images. Therefore, a transformation maps each pre-image point to its image point.

Reflections

Reflections are transformations that involve "flipping" points over a given line; hence, this type of transformation is sometimes called a "flip." When a figure is reflected in a line, the points on...