Chapter 14.8, Problem 4WE

a.

To determine

To state how many symmetry line the figure has.

Answer to Problem 4WE

The figure has thirteen lines of symmetry.

Explanation of Solution

Given information:

The given statement is that consider the figure as a plane figure.

The figure has thirteen lines of symmetry. The figure has thirteen regular wing connected from the centre of figure. Each symmetry line passes through the centre and bisects one wing vertically.

b.

To determine

To state whether or not the figure has a symmetry point.

Answer to Problem 4WE

The figure has no symmetry point.

Explanation of Solution

Given information:

The given statement is that consider the figure as a plane figure.

Since, a point symmetry is nothing but a rotational symmetry of $180°$ and the figure is not symmetric at a rotation of $180°$ . Hence the figure has no symmetry point.

c.

To determine

To list all the rotational symmetries of each figure between $0°\text{ and 360}°$ .

Answer to Problem 4WE

The figure has rotational symmetry at $27.7°,55.4°,83°,110.8°,138.5°,166.2°,193.9°,221.5°,249.3°,277°,304.7°,332.8°\text{ and }360°$ .

Explanation of Solution

Given information:

The given statement is that consider the figure as a plane figure.

The figure has thirteen regular wings therefore the rotational symmetry can be obtained at

$\frac{\text{360}°}{13}=27.7°$

If the figure is symmetric at $27.7°$ then it is also symmetric about the angles which are multiples of $27.7°$ . Hence the figure hasrotational symmetry at $27.7°,55.4°,83°,110.8°,138.5°,166.2°,193.9°,221.5°,249.3°,277°,304.7°,332.8°\text{ and }360°$ .