Rotate points through 45 degrees about the point (3,7). Then calculate where the point (0,5) would now be after the transformations.
So I was able to do the first part of the problem that gives the 3x3 transformation matrix (see work below). But to do the second part of the question, would I just multiply the 3x3 transformation matrix by (0, 5, 1)? If not, how would I do it?
\begin{equation} \begin{pmatrix} 1 & 0 & 3 \\ 0 & 1 & 7 \\ 0 & 0 & 1 \end{pmatrix} \times \begin{pmatrix} \sqrt{2}/2 & -\sqrt{2}/2 & 0 \\ \sqrt{2}/2 & \sqrt{2}/2 & 0 \\ 0 & 0 & 1 \end{pmatrix} \times \begin{pmatrix} 1 & 0 & -3 \\ 0 & 1 & -7 \\ 0 & 0 & 1 \\ \end{pmatrix} \end{equation}
= \begin{pmatrix} \sqrt{2}/2 & -\sqrt{2}/2 & 3+2\sqrt{2} \\ \sqrt{2}/2 & \sqrt{2}/2 & -\sqrt{2}/2 \\ 0 & 0 & 1 \end{pmatrix}