Chapter 14.4, Problem 9WE

To determine

To find: Pre-image of point $O$ from rotation $R_{D,60}$ .

Answer to Problem 9WE

Pre-image of point $O$ after rotation i.e. $R_{D,60}$ is $C$ .

Explanation of Solution

Given information :

  $O$ is centre of hexagon $ABCDEF$ . Rotation is $R_{D,60}$ .

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 D through ${60}^o$ counter-clockwise represent as $R_{D,60}$ .

  

Diagram as per the question

  

  $ABCDEF$ is a regular hexagon.

  $\angle AOF=\angle FOE=\angle EOD=\angle DOC=\angle COB=\angle BOA={60}^{{\rm O}}$

  $\Delta COD$ is an equilateral triangle

  $\angle DOC=\angle OCD=\angle CDO={60}^{°}$

  $R_{D,60}:C\to O$

Hence,

Pre-image of point $O$ after rotation i.e. $R_{D,60}$ is $C$ .