Chapter 14.8, Problem 2WE

a.

To determine

To state how many symmetry line the figure has.

Answer to Problem 2WE

The figure has six lines of symmetry.

Explanation of Solution

Given information:

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

The figure has six lines of symmetry. Three lines passing through the centre of the figure and connecting the opposite corners of the hexagon which is inside the figure. And other three passing through centre and bisects opposite sides of the hexagon.

b.

To determine

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

Answer to Problem 2WE

The figure has the 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 symmetric at a rotation of $180°$ . Hence the figure has the symmetry point.

c.

To determine

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

Answer to Problem 2WE

The figure has rotational symmetry at $60°,120°,180°,240°,300°\text{ and }360°$ .

Explanation of Solution

Given information:

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

The figure has six regular extensions therefore the rotational symmetry can be obtained at

  $\frac{\text{360}°}{6}=60°$

If the figure is symmetric at $60°$ then it is also symmetric about the angles which are multiples of $60°$ . Hence the figure hasrotational symmetry at $60°,120°,180°,240°,300°\text{ and }360°$ .