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

A reflection across SR flips the figure in a certain way, then a 90 - counter - clockwise rotation around S changes its orientation. Visualize the two - step transformation. The first step flips the figure over SR, and the second step rotates it. This combination does not map PQRS onto PNM S.

Step2: Analyze Option B

A reflection across PQ flips the figure. Then a 90 - counter - clockwise rotation around P re - orients it. When we perform these two transformations, we can see that figure PQRS is mapped onto figure PNM S.

Step3: Analyze Option C

A 90 - counter - clockwise rotation around S changes the orientation of PQRS. Then a reflection across SP' re - arranges it. By visualizing these two steps, we find that PQRS is mapped onto PNM S.

Step4: Analyze Option D

A 180 - counter - clockwise rotation around S flips the figure in a 180 - degree turn. Then a reflection across SR' further modifies it. This combination does not map PQRS onto PNM S.

Answer:

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'.