Translation
The translation of figure ABCDEF to the left 20 units and down 6 units can be proven accurate without the use of a coordinate plane because each vertex has been moved in the same distance and direction. The points have been moved parallel to the vector of the translation to form the image, and lines drawn from each vertex on figure ABCDEF to its image will be parallel to that vector. Since translations are a type of rigid motion and do not alter a figure’s size or shape, figure A’B’C’D’E’F’ can be mapped back onto pre-image ABCDEF by a translation of 20 units to the right and 6 units up to prove that this translation is accurate.