Question

a regular hexagon is rotated 360° about its center. how many times does the image of the hexagon coincide with the pre - image during the rotation?
a. 1 time
b. 6 times
c. 3 times
d. 12 times

Explanation:

Step1: Determine the rotational - symmetry order of a regular hexagon

A regular hexagon has rotational - symmetry. The angle of rotational symmetry of a regular polygon is given by $\frac{360^{\circ}}{n}$, where $n$ is the number of sides of the polygon. For a hexagon, $n = 6$, and the angle of rotational symmetry is $\frac{360^{\circ}}{6}=60^{\circ}$.

Step2: Calculate the number of times it coincides in a 360 - degree rotation

To find out how many times the hexagon coincides with its pre - image during a $360^{\circ}$ rotation, we divide the total angle of rotation ($360^{\circ}$) by the angle of rotational symmetry ($60^{\circ}$). So, $\frac{360^{\circ}}{60^{\circ}} = 6$.

Answer:

B. 6 times