Problem
15. Find the coordinates of the vertices of the rectangle $W X Y Z$ with coordinates $W(11,-5), X(9,3), Y(-2,8), Z(-1,-4)$ after a dilation with a scale factor of 6 . Write the answer as a matrix. $\left[\begin{array}{cccc}-5 & -3 & 8 & 7 \\ 11 & 3 & -2 & 10\end{array}\right]$ $\left[\begin{array}{cccc}11 & 9 & -2 & -1 \\ -5 & 3 & 8 & -4\end{array}\right]$ $\left[\begin{array}{cccc}17 & 15 & 4 & 5 \\ 1 & 9 & 14 & 2\end{array}\right]$ $\left[\begin{array}{cccc}66 & 54 & -12 & -6 \\ -30 & 18 & 48 & -24\end{array}\right]$
Solution
Step 1 ：The dilation centered at the origin with scale factor 6 takes \(\begin{pmatrix} 11 \\ -5 \end{pmatrix}\) to \(\begin{pmatrix} 66 \\ -30 \end{pmatrix}\), \(\begin{pmatrix} 9 \\ 3 \end{pmatrix}\) to \(\begin{pmatrix} 54 \\ 18 \end{pmatrix}\), \(\begin{pmatrix} -2 \\ 8 \end{pmatrix}\) to \(\begin{pmatrix} -12 \\ 48 \end{pmatrix}\), and \(\begin{pmatrix} -1 \\ -4 \end{pmatrix}\) to \(\begin{pmatrix} -6 \\ -24 \end{pmatrix}\).
Step 2 ：So the matrix is \(\boxed{\begin{pmatrix} 66 & 54 & -12 & -6 \\ -30 & 18 & 48 & -24 \end{pmatrix}}\).
