Question

use the graph below to answer the question. quadrilateral pqrs will be rotated 90° clockwise about the origin resulting in quadrilateral pqrs. which statement is true? a rs will be parallel to rs b sp will be parallel to rs c the measure of ∠p will be 80° d the measure of ∠q will be 80°

Explanation:

Step1: Recall rotation property

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve side lengths and angle measures, and parallel lines remain parallel after rotation.

Step2: Analyze each option

• Option A: When a figure is rotated, parallel lines in the original figure are parallel to the corresponding lines in the rotated figure. $\overline{RS}$ and $\overline{R'S'}$ are corresponding sides, so $\overline{RS}$ will be parallel to $\overline{R'S'}$.
• Option B: $\angle P = 60^{\circ}$, and rotation preserves angle measures. So the measure of $\angle P'$ will be $60^{\circ}$, not $80^{\circ}$.
• Option C: $\overline{SP}$ and $\overline{R'S'}$ are not corresponding sides in a way that would guarantee parallelism.
• Option D: $\angle Q = 80^{\circ}$, and rotation preserves angle measures. But this option just states the measure of $\angle Q'$ without being the most relevant property about the rotation of the quadrilateral.

Answer:

A. $\overline{RS}$ will be parallel to $\overline{R'S'}$