Question

figures pqrs and pnms are congruent. select all of the sequences of transformations that will carry figure pqrs onto figure pnms. a. a reflection of pqrs across side sr followed by a 90° counter - clockwise rotation around point s. b. a reflection of pqrs across side pq followed by a 90° counter - clockwise rotation around point p. c. a rotation of pqrs by 90° counter - clockwise around point s followed by a reflection across side sp. d. a rotation of pqrs by 180° counter - clockwise around point s, followed by a reflection across side sr.

Explanation:

Step1: Analyze Option A

1. Reflect $PQRS$ across $SR$. This flips the figure over the line $SR$.
2. Then rotate the reflected figure $90^{\circ}$ counter - clockwise around $S$. This will map $PQRS$ onto $PNMS$.

Step2: Analyze Option B

1. Reflect $PQRS$ across $PQ$. The orientation of the figure after reflection is not correct for the subsequent rotation to map it onto $PNMS$.

Step3: Analyze Option C

1. Rotate $PQRS$ $90^{\circ}$ counter - clockwise around $S$.
2. Then reflect the rotated figure across $SP'$. This sequence of transformations will map $PQRS$ onto $PNMS$.

Step4: Analyze Option D

1. Rotate $PQRS$ $180^{\circ}$ counter - clockwise around $S$.
2. After reflection across $SR'$, the figure will not be mapped onto $PNMS$.

Answer:

A. A reflection of $PQRS$ across side $SR$ followed by a $90^{\circ}$ counter - clockwise rotation around point $S$.
C. A rotation of $PQRS$ by $90^{\circ}$ counter - clockwise around point $S$ followed by a reflection across side $SP'$.