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:

Step1: Analyze each figure's symmetry

• First figure (triangle): It is an isosceles triangle, which has reflectional symmetry (along the altitude from the apex) but rotational symmetry of order 1 (only 360° rotation, which is trivial), so it has reflectional symmetry.
• Second figure (three rectangles): Let's check rotational symmetry: If we rotate the figure by 120° (since there are 3 rectangles), it maps onto itself, so it has rotational symmetry of order 3. Now check reflectional symmetry: There is no line that can reflect the figure onto itself (the rectangles are arranged in a rotational pattern without a mirror line), so it has rotational symmetry but not reflectional symmetry.
• Third figure (diamond - rhombus): A rhombus has both rotational symmetry (order 2) and reflectional symmetry (along its diagonals).
• Fourth figure (two ellipses crossing): This figure has both rotational symmetry (order 2 or more) and reflectional symmetry (along the axes of the ellipses).

Step2: Identify the correct figure

From the analysis, the figure with three rectangles (the second option) has rotational symmetry but not reflectional symmetry.

Answer:

The option with the three rectangles (the second figure among the choices) is the correct one. (Assuming the options are labeled as first, second, third, fourth with the second being the three rectangles) If we consider the options as, say, A (triangle), B (three rectangles), C (rhombus), D (ellipses), then the answer is B. Option Text (the one with three rectangles arranged rotationally).