Question

the image is an example of which type(s) of symmetry?
a. reflectional
b. rotational
c. both rotational and reflectional
d. neither rotational nor reflectional

Explanation:

1. Reflectional Symmetry Check: A figure has reflectional symmetry if there is a line (axis of symmetry) such that reflecting the figure over that line maps it onto itself. The given figure (a regular pentagon - like shape with axes drawn) has multiple lines of symmetry (the drawn lines) where reflecting over them would match the figure.
2. Rotational Symmetry Check: A figure has rotational symmetry if rotating it about a central point by a certain angle (less than \(360^\circ\)) maps it onto itself. For a regular pentagon (or this symmetric shape), rotating it by \(\frac{360^\circ}{5}=72^\circ\) (or multiples) about the center will map it onto itself, so it has rotational symmetry.

Since it has both reflectional (due to axes of symmetry) and rotational symmetry, the correct option is C.

Answer:

C. Both rotational and reflectional