transformations

point H is located at (-7,5).

Where is H after a 270 degrees clockwise rotation?

\(\begin{array}{|rcll|} \hline \begin{pmatrix} -7 \\ 5 \end{pmatrix} \cdot \begin{pmatrix} \cos(270^{\circ}) & -\sin(270^{\circ}) \\ \sin(270^{\circ}) & \cos(270^{\circ}) \\ \end{pmatrix} &=& \begin{pmatrix} -7 \\ 5 \end{pmatrix} \cdot \begin{pmatrix} 0 & 1 \\ -1 & 0\\ \end{pmatrix} \\ &=& \begin{pmatrix} -7\cdot 0 + 5\cdot(-1) \\ -7\cdot 1 + 5\cdot 0 \end{pmatrix} \\ &=& \begin{pmatrix} -5 \\ -7 \end{pmatrix} \\ \hline \end{array} \)

H after a 270 degrees clockwise rotation is at  (-5,-7)