Chapter 14.4, Problem 13WE

To determine

To find: $R_K(A)$

Answer to Problem 13WE

  $R_K(A)={90}^{°}$ .

Explanation of Solution

Given information:

  $O$ is centre of hexagon $ABCDEF$ . Rotation is $R_K(A)$ .

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

  $R_K(A)$ where K is perpendicular bisector of $\overleftrightarrow{FE}$ .

  

Diagram as per the question

  

  $ABCDEF$ is aregular hexagon.

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

  $R_K(A)={90}^{°}$

Rotation of $A$ from the point $K$ on $\overleftrightarrow{FE}$ is $\angle AOF+\frac{\angle FOE}{2}=\angle AOF+\angle FOK={60}^{°}+\frac{{60}^{°}}{2}={90}^{°}$ .

Hence,

  $R_K(A)={90}^{°}$.