Chapter 8.4, Problem 92AE

Computer Graphics: Translating An important aspect of computer graphics is the ability to transform the coordinates of points within a graphic. For transformation purposes, a point $\left(x,y\right)$ is represented as the column matrix $X\text{ = }\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]$.

To translate a point $\left(x,y\right)$ $h$ units and vertically $k$ units , we use the translation matrix $s\text{ = }\left[\begin{array}{c}1\\ 0\\ 0\end{array}\begin{array}{c}0\\ 1\\ 0\end{array}\begin{array}{c}h\\ k\\ 1\end{array}\right]$ and

compute the matrix product $SX$. The translation is to the right for $h\text{ > 0}$ and to the left for $h\text{ < 0}$. Likewise, the translation is up for and down for . The transformed coordinates are the first two entries in the resulting column matrix.

a. Write the translation matrix needed to translate a point 3 units to the left and 5 units up.

b. Find and interpret $S^{-1}$.