Question

use the figure shown.
which rotation maps the figure onto itself?
a. ( r_{(45^{circ}, p)} )
b. ( r_{(90^{circ}, p)} )
c. ( r_{(180^{circ}, p)} )
d. ( r_{(270^{circ}, p)} )

Explanation:

Step1: Recall the property of rotational symmetry

A figure has rotational symmetry if it maps onto itself when rotated by a certain angle about a center point.

Step2: Analyze each option

• For \(R(45^{\circ},P)\): Rotating the figure by \(45^{\circ}\) about point \(P\) will not map the figure onto itself.
• For \(R(90^{\circ},P)\): Rotating the figure by \(90^{\circ}\) about point \(P\) will not map the figure onto itself.
• For \(R(180^{\circ},P)\): Rotating the figure by \(180^{\circ}\) about point \(P\) (a half - turn) will map the figure onto itself.
• For \(R(270^{\circ},P)\): Rotating the figure by \(270^{\circ}\) about point \(P\) will not map the figure onto itself.

Answer:

C. \(R(180^{\circ},P)\)