Question

which rule describes the composition of transformations that maps figure pqrs to figure p\q
\s\?
○ 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 there is a rotation about point $Q$ by $180^{\circ}$ which changes the orientation of the figure. Then, there is a reflection across line $l$. The notation for composition of transformations $A\circ B$ means perform transformation $B$ first and then transformation $A$. So we need to first perform the rotation about $Q$ by $180^{\circ}$ and then the reflection across line $l$.

Step2: Identify the correct notation

The rotation about point $Q$ by $180^{\circ}$ is denoted as $R_{Q,180^{\circ}}$ and the reflection across line $l$ is denoted as $r_{l}$. The correct composition is $r_{l}\circ R_{Q,180^{\circ}}$.

Answer:

$r_{l}\circ R_{Q,180^{\circ}}$