Chapter 14.4, Problem 6CE

To determine

To find: Images of points $P,S\&T$ after rotation.

Answer to Problem 6CE

Images of $P$ is $T$ , $T$ is $S$ & $S$ is $P$ .

Explanation of Solution

Given information :

  $O$ is centre of equilateral $\Delta PST$ . Rotation is $R_{O,120}$ .

Concept used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

As per the given problem

A rotation about a point O through ${120}^o$ counter-clockwise represent as $R_{O,120}$ .

  

Diagram as per the question

  

  $\Delta PST$ is an equilateral triangle.

  $\angle POS=\angle TOS=\angle POT={120}^{{\rm O}}$

  $\begin{array}{l}{R}_{O,120}(S)=P\\ R_{O,120}(T)=S\\ R_{O,120}(P)=T\end{array}$

Hence,

Images of $P$ is $T$ , $T$ is $S$ & $S$ is $P$ .