Question

which rule describes the composition of transformations that maps figure pqrs to figure pqrs?
r o rl
rl o rq, 180°
rq, 180° o rs, 270°
rs, 270° o rq, 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 means the transformation on the right - hand side is done first. So, the rotation about $Q$ by $180^{\circ}$ ($R_{Q,180^{\circ}}$) is done first and then the reflection across line $l$ ($r_{l}$).

Step2: Match with options

The correct composition of transformations is $r_{l}\circ R_{Q,180^{\circ}}$.

Answer:

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