Chapter 14.7, Problem 9WE

To determine

To give : the image of $A$ under rotation of $R^{-2}$ .

Explanation of Solution

Given information : The rotation $R$ maps all points ${90}^{\circ }$ about $O$ , the centre of square $ABCD$ .

From the above figure it is observed that:

  $\begin{array}{l}{R}^{-1}\left(A\right)\\ \Rightarrow R\left(R^{-1}\left(A\right)\right)\\ \Rightarrow R\left(D\right)\\ \Rightarrow A\\ R^{-2}\left(A\right)\\ \Rightarrow C\end{array}$