Chapter 14.8, Problem 7CE

To determine

To describe all the rotational symmetries of the figure.

Answer to Problem 7CE

The figureX has 4 rotational symmetry.

Explanation of Solution

Given information:

The figure of X .

The figure ofX has the four rotational symmetry. Each symmetry has center O and rotates the figure onto itself. Note that $90°$ rotational symmetry is another name for point symmetry.

  $\begin{array}{l}\left(1\right)\text{ 9}0°{\text{ rotational symmetry: R}}_{0,90}\\ \left(2\right)\text{ 18}0°{\text{ rotational symmetry: R}}_{0,1800}\\ \left(3\right)\text{ 27}0°{\text{ rotational symmetry: R}}_{0,270}\\ \left(4\right)\text{ 36}0°\text{ rotational symmetry: I is the identity}\text{.}\end{array}$

The identity mapping always maps a figure onto itself, we usually include the identity when listing the symmetries of a figure.

Therefore, the figure X has 4 rotational symmetry.