### Rotations of multiples of 90 ° about a point

In the figure above, \(\triangle ABC\) is rotated 90 ° in a clockwise direction about point \(D\) to the image \(\triangle A^\prime B^\prime C^\prime\).

The point \(A\) in the diagram above is rotated 90 ° in a clockwise direction about point \(D\). Note that \(AD = A^\prime D\) and \(\angle AD A^\prime = 90^\circ\).

Using coordinates we can describe the rotation of the vertices:

\(A(4, 4) \rightarrow A^\prime (9, 3); B(3, 6) \rightarrow B^\prime (7, 2); C(5, 7) \rightarrow C^\prime (6, 4)\).