Question

Which is the image of ABC for a 90° counterclockwise rotation about P?

Answer 1

Let \([x_n,y_n]^T\) for \(n=1,2,3\) be the points of \(ABC\). Then
\[\begin{bmatrix}
\cos\theta & -\sin\theta\\
\sin\theta & \cos\theta
\end{bmatrix}\begin{bmatrix}
x_n\\
y_n
\end{bmatrix}\]is the clockwise \(90^\circ\) rotation of \(ABC\) about the origin. It is not difficult to generalize this for about a point \(P\).