Question

describe the rotational symmetry of the figure.
image of a yellow diamond-shaped sign with a black cross
options:

• 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°
• 60°, 120°, 180°, 240°
• 90°, 180°, 270°
• 180°

Explanation:

Step1: Recall Rotational Symmetry

Rotational symmetry means a figure can be rotated by an angle and map onto itself. For a square (the diamond shape with a cross, which is like a square with a symmetric cross), the order of rotational symmetry is 4 (since a square has 4 equal sides/angles). The angle of rotational symmetry is \( \frac{360^\circ}{n} \), where \( n \) is the order. For \( n = 4 \), the angle is \( 90^\circ \). So the figure should map onto itself when rotated by \( 90^\circ \), \( 180^\circ \) (which is \( 90^\circ\times2 \)), \( 270^\circ \) (which is \( 90^\circ\times3 \)), and \( 360^\circ \) (the full rotation, but usually we consider angles less than \( 360^\circ \) for non - full rotations).

Step2: Analyze the Options

• Option 1: Angles like \( 30^\circ, 60^\circ \) etc. don't fit because the figure's rotational symmetry angle is based on a square's symmetry ( \( 90^\circ \) increments).
• Option 2: \( 60^\circ \) increments are for a figure with order 6 (like a regular hexagon), not a square - like figure. So this is incorrect.
• Option 3: \( 90^\circ, 180^\circ, 270^\circ \) are the angles by which the figure (a square - like shape with a symmetric cross) will map onto itself.
• Option 4: Only \( 180^\circ \) is too restrictive, as the figure also has symmetry at \( 90^\circ \) and \( 270^\circ \).

Answer:

\( 90^\circ \), \( 180^\circ \), \( 270^\circ \) (the option with \( 90^\circ \), \( 180^\circ \), \( 270^\circ \))