Question

which rule describes the composition of transformations that maps figure pqrs to figure pqrs? options: ( r_{q, 180^circ} circ r_{s, 270^circ} ), ( r_{s, 270^circ} circ r_{q, 180^circ} ), ( r_l circ r_{q, 180^circ} ), ( r circ r_l ) (diagram includes figures pqrs, ( pqrs ), ( pqrs ), and line ( l ) with a red arrow.)

Explanation:

Step1: Identify transformations

Assume PQRS → P'Q'R'S' via R_Q, 180° (rotate 180° about Q), then P'Q'R'S' → P''Q''R''S'' via R_S', 270° (rotate 270° about S').

Step2: Composition order

Compositions apply right-to-left: first R_Q, 180°, then R_S', 270°, so R_S', 270° ∘ R_Q, 180°.

Answer:

R_S', 270° ∘ R_Q, 180°