Question

figure pqrst shown in the coordinate grid is translated 3 units down and 2 units to the right. then it is reflected in the y-axis to form pqrst. which statements are true? choose all that apply. a ∠s ≅ ∠s b (overline{pt} cong overline{pt}) c the area of pqrst is greater. d the perimeter of pqrst is greater. e the figures’ orientations are the same. f the figures are congruent.

Explanation:

• Option A: Translations and reflections are rigid transformations, so angle measures are preserved. Thus, $\angle S \cong \angle S'$.
• Option B: Rigid transformations preserve segment lengths, so $\overline{PT} \cong \overline{P'T'}$.
• Option C: Rigid transformations do not change the area of a figure, so the area of $P'Q'R'S'T'$ is equal to the area of $PQRST$, not greater.
• Option D: Rigid transformations preserve the perimeter of a figure, so the perimeter of $PQRST$ is equal to the perimeter of $P'Q'R'S'T'$, not greater.
• Option E: A reflection over the $y$-axis changes the orientation of the figure (e.g., left - right orientation flips), so the orientations are not the same.
• Option F: Translations and reflections are rigid transformations, and rigid transformations produce congruent figures. So $PQRST$ and $P'Q'R'S'T'$ are congruent.

Answer:

A. $\angle S \cong \angle S'$
B. $\overline{PT} \cong \overline{P'T'}$
F. The figures are congruent.