Chapter 14.7, Problem 14CE

To determine

To give : the image of $A$ under rotation of $R^6$ .

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:

  $\begin{array}{l}{R}^3\left(A\right)=R\left(R\left(R\left(A\right)\right)\right)\\ \Rightarrow R\left(R\left(B\right)\right)=R\left(C\right)\\ \Rightarrow R\left(C\right)=A\\ R^6\left(A\right)={\left(R^3\right)}^2\left(A\right)=\\ \Rightarrow I^2\left(A\right)=A\end{array}$