Question

which rule describes the composition of transformations that maps δabc to δabc?
r_m ∘ r_{b, 90°}
r_{b, 90°} ∘ r_m
r_m ∘ r_{b, 270°}
r_{b, 270°} ∘ r_m

Explanation:

Step1: Analyze transformation order

First, observe that $\triangle ABC$ is rotated about point $B'$ and then reflected over line $m$. The notation for composition of transformations has the right - hand transformation performed first.

Step2: Determine rotation angle

The rotation from $\triangle ABC$ to an intermediate position (before reflection) is a $90^{\circ}$ counter - clockwise rotation about point $B'$, denoted as $R_{B',90^{\circ}}$. Then the reflection over line $m$ is denoted as $r_m$. So the composition is $r_m\circ R_{B',90^{\circ}}$.

Answer:

$r_m\circ R_{B',90^{\circ}}$