Question

a student drew a picture that has rotational symmetry but not reflectional symmetry. which of the following could be the figure that the student drew?

Explanation:

1. Analyze the butterfly figure: It has reflectional symmetry (along the vertical axis through its center) but rotational symmetry of order 1 (only 360° rotation), so it doesn't meet the "rotational but not reflectional" condition.
2. Analyze the yellow pinwheel - like figure: It has rotational symmetry (e.g., order 4, as rotating 90° maps it onto itself) and no reflectional symmetry (no line that can reflect it onto itself).
3. Analyze the blue trapezoid - like figure: It has reflectional symmetry (vertical axis through the center) and rotational symmetry of order 1, so it doesn't meet the condition.
4. Analyze the octagon: It has both rotational symmetry (multiple orders) and reflectional symmetry (multiple lines), so it doesn't meet the condition.

Answer:

The second option (the yellow pinwheel - like figure in the black square)