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 transformation sequence

First, observe that there is a rotation \(R_{Q,180^{\circ}}\) (rotation about point \(Q\) by \(180^{\circ}\)) which maps \(PQRS\) to an intermediate figure. Then, there is a reflection \(r_{l}\) (reflection over line \(l\)) which maps the intermediate figure to \(P''Q''R''S''\). The composition of transformations is written with the right - most transformation performed first. So the composition is \(r_{l}\circ R_{Q,180^{\circ}}\)

Answer:

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