Question

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

Explanation:

Step1: Calculate the angle of rotational symmetry

For a regular polygon with \(n\) sides, the angle of rotational symmetry \(\theta=\frac{360^{\circ}}{n}\). For a hexagon, \(n = 6\), so \(\theta=\frac{360^{\circ}}{6}=60^{\circ}\).

Step2: Determine the number of coincidences

The number of times the pre - image and image coincide during a \(360^{\circ}\) rotation is given by \(\frac{360^{\circ}}{\theta}\). Since \(\theta = 60^{\circ}\), \(\frac{360^{\circ}}{60^{\circ}}=6\).

Answer:

A. 6 times