Chapter 14.4, Problem 12WE

To determine

To find: Reflection in $\overleftrightarrow{FC}$ maps to $B\&D$ .

Answer to Problem 12WE

A reflection in $\overleftrightarrow{FC}$ maps $B$ to $D$ & $D$ to $B$ .

Explanation of Solution

Given information :

  $O$ is centre of hexagon $ABCDEF$ . Rotation is $H_O$ .

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

Reflection in $\overleftrightarrow{FC}$ needs to be used to find mapping points.

  

Diagram as per the question

  

  $ABCDEF$ is a regular hexagon.

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

  $\begin{array}{l}{R}_M:\overleftrightarrow{FC}(B)\to D\\ R_M:\overleftrightarrow{FC}(D)\to B\end{array}$

Reflection means mirror image of points w.r.t the reflection line. Point $B$ & $D$ are equidistant from reflection line $\overleftrightarrow{FC}$ .

Hence,

A reflection in $\overleftrightarrow{FC}$ maps $B$ to $D$ & $D$ to $B$ .