Chapter 14.4, Problem 9CE

To determine

To find: Images of point $S$ after rotation.

Answer to Problem 9CE

Images of $S$ is $P$ for $R_{T,60}$ .

Explanation of Solution

Given information :

  $O$ is centre of equilateral $\Delta PST$ . Rotation is $R_{T,60}$ .

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 ${60}^o$ clockwise represent as $R_{O,60}$ .

  

Diagram as per the question

  

  $\Delta PST$ is an equilateral triangle.

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

  $\angle PST=\angle STP=\angle TPS={60}^{{\rm O}}$

  $R_{T,60}(S)=P$

i.e. Rotation of $S$ counter-clockwise ${60}^o$ at a point $T$ will be $P$ .

Hence,

Image of $S$ is $P$ for $R_{T,60}$ .