Chapter 14.7, Problem 18CE

To determine

To give : the image of $A$ under rotation of $R^2\cdot R^{-3}$ .

Explanation of Solution

Given information : The rotation $R$ maps all points ${120}^{\circ }$ about $G$ , the centre of equilateral $\Delta ABC$ .

From the above figure it is observed that:

  $\begin{array}{l}{R}^2\cdot R^{-3}\\ \Rightarrow R^2\left(R^{-3}\left(A\right)\right)\\ \Rightarrow R^2\left(A\right)\\ \Rightarrow R\left(R\left(A\right)\right)\\ \Rightarrow R\left(A\right)=C\end{array}$