Question

question 5 of 10

the image is an example of which type(s) of symmetry?

a. rotational
b. neither rotational nor reflectional
c. reflectional
d. both rotational and reflectional

Explanation:

Analyze reflectional symmetry

The image shows a regular pentagon with lines drawn through its center. A regular pentagon has 5 lines of reflectional symmetry, each passing through a vertex and the midpoint of the opposite side. Since these lines map the figure onto itself, it has reflectional symmetry.

Analyze rotational symmetry

A regular pentagon can be rotated about its center by multiples of \(72^\circ\) (since \(\frac{360^\circ}{5} = 72^\circ\)) to map onto itself. Because there is a non-trivial rotation (less than \(360^\circ\)) that leaves the figure unchanged, it has rotational symmetry.

Determine the correct option

Since the figure possesses both types of symmetry, the correct choice is "Both rotational and reflectional".

Answer:

• (A) Rotational
• (B) Neither rotational nor reflectional
• (C) Reflectional
• (D) Both rotational and reflectional (Correct answer)