Question

1. does the following figure have both rotational and reflectional symmetry? why or why not?

Explanation:

To determine symmetry:

• Reflectional Symmetry: A heart has a vertical line of symmetry (left - right mirror image matches).
• Rotational Symmetry: For rotational symmetry, a figure must map onto itself after rotating less than \(360^\circ\). A heart, when rotated (e.g., \(180^\circ\)), does not look the same (the pointed bottom and curved top change orientation), so it has no rotational symmetry.

Answer:

The heart - shaped figure has reflectional symmetry (due to a vertical line of symmetry) but not rotational symmetry (it does not map onto itself when rotated by an angle less than \(360^\circ\)). So, it does not have both rotational and reflectional symmetry.