A translation is one of the three transformations that move a figure in the plane without changing its size or shape. (The other two are rotations and reflections.) In a translation, the figure is moved in a single direction without turning it or flipping it over.

A translation can, of course, be combined with the two other rigid motions (as transformations which preserve a figure's size and shape are called), and it can in particular be combined with another translation. The "product" of two translations is also a translation, as illustrated in Figure 2.

If a set of points is drawn on a coordinate plane, it is a simple matter to write equations which will connect a point (x,y) with its translated "image" (x^1,y¹). If a point has been moved a units to the right or left and b units up or down, a will be added...