Question

which rule describes the composition of transformations that maps figure pqrs to figure pqrs?
r∘r₁
r₁∘r_q,180°
r_q,180°∘r_s,270°
r_s,270°∘r_q,180°

Explanation:

Step1: Analyze the transformations

First, observe that figure PQRS is rotated 180° about point Q to get an intermediate - figure (let's call it P'Q'R'S'). Then, this intermediate - figure is reflected across line l. The notation for rotation about a point Q by 180° is \(R_{Q,180^{\circ}}\) and the notation for reflection across a line l is \(r_{l}\). The composition of transformations is written with the transformation that is done first on the right - hand side of the composition symbol \(\circ\). So the composition of rotation about Q by 180° first and then reflection across line l is \(r_{l}\circ R_{Q,180^{\circ}}\).

Answer:

\(r_{l}\circ R_{Q,180^{\circ}}\)