A transformation is a one-to-one function that maps a set of points onto another set of points. The "points" mentioned here may be one-dimensional points on the real number line, two-dimensional points in the plane, three-dimensional points in Euclidean space, or any higher dimensional points in abstract space. We shall confine ourselves to one and two dimensions in this article. The points in the domain of the translation are often called "pre-images," while points in the range are called "images." The mathematical formula that describes how to map pre-images to images is sometimes called a "transformation image formula." From a practical point of view, we may say that a transformation is a function that repositions points. For example, the one-dimensional transformation T(x) = x + 3 repositions any point on the real number line three units to the right. This particular transformation is called a translation. The transformation T(x...