Question

is it possible for a figure to have reflectional symmetry and no rotational symmetry? explain or give examples.

choose the correct answer below

a. no. it is not possible. if a figure has reflectional symmetry, it must have rotational symmetry because a rotation is a composition of two reflections.

b. no. it is not possible. if a figure has reflectional symmetry, it must have point symmetry, which is a special case of rotational symmetry. since every line of symmetry of a figure passes through the center of the figure, the figure must be symmetric about that point.

c. no. it is not possible. if a figure has reflectional symmetry it must have rotational symmetry. the letters h, o, and x are examples of this.

d. yes. it is possible for a figure to have reflectional symmetry without having rotational symmetry. the letters a, d, and w are examples of this.

Explanation:

To determine the answer, we analyze each option:

• Option A: A rotation being a composition of two reflections is true, but this doesn't mean a figure with reflectional symmetry must have rotational symmetry (e.g., letter A has reflectional symmetry but not rotational symmetry matching its reflectional axis). So A is incorrect.
• Option B: Not all figures with reflectional symmetry have point symmetry (e.g., letter A). So B is incorrect.
• Option C: Letters H, O, X have both reflectional and rotational symmetry, but this doesn't mean all figures with reflectional symmetry do. So C is incorrect.
• Option D: Letters A, D, W have a vertical line of reflectional symmetry. When rotated (e.g., 180 degrees), they don't map onto themselves, so they have no rotational symmetry. This shows it is possible.

Answer:

D. Yes. It is possible for a figure to have reflectional symmetry without having rotational symmetry. The letters A, D, and W are examples of this.