Chapter 14.7, Problem 7WE

To determine

To give : the image of $A$ under rotation of $R^4$ .

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:

  $\begin{array}{l}{R}^2\left(A\right)\\ \Rightarrow R\left(R\left(A\right)\right)\\ \Rightarrow R\left(B\right)\\ \Rightarrow C\\ R^3\left(A\right)\\ \Rightarrow R\left(R^2\left(A\right)\right)\\ \Rightarrow R\left(C\right)\\ \Rightarrow D\\ R^4\left(A\right)\\ \Rightarrow R\left(R^3\left(A\right)\right)\\ \Rightarrow R\left(D\right)\\ \Rightarrow A\end{array}$