Chapter 14.4, Problem 14WE

To determine

To find: Mapping of $O\&E$ .

Answer to Problem 14WE

If translation maps $A$ to $B$ , then maps $O$ to $O$ & $E$ to $F$ .

Explanation of Solution

Given information :

  $O$ is centre of hexagon $ABCDEF$ . Translation maps $A$ to $B$ .

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, translation maps $A$ to $B$ .

Diagram as per the question

  

  $ABCDEF$ is a regular hexagon.

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

  $R_{O,60}:A\to B$

This shows, translation of $A$ to $B$ under the point $O$ counter-clockwise ${60}^{°}$ .

  $\begin{array}{l}{R}_{O,60}:O\to O\\ R_{O,60}:E\to F\end{array}$

Hence,

If translation maps $A$ to $B$ , then maps $O$ to $O$ & $E$ to $F$ .