An important aspect of computer graphics is the ability to transform the coordinates of points within a graphic. For transformation purposes, a point (x, y) is represented as the column matrix

To translate a point (x, y) horizontally h units and vertically k units, we use the translation matrix

and compute the matrix product SX. The translation is to the right for h > 0 and to the left for h up for k > 0 and down for k (a) Write the translation matrix needed to translate a point 3 units to the left and 5 units up.
(b) Find and interpret S⁻¹.

X || X y 1