Question

which rule describes the composition of transformations that maps △abc to △a\bc\?
○ rₘ ∘ r₉₀°
○ r₉₀° ∘ rₘ
○ rₘ ∘ r₂₇₀°
○ r₂₇₀° ∘ rₘ

Explanation:

Step1: Analyze rotation

First, observe that from $\triangle ABC$ to $\triangle A'B'C'$, it seems to be a $90 - degree$ rotation about point $B$. The notation for a $90 - degree$ rotation about point $B$ is $R_{B,90^{\circ}}$.

Step2: Analyze reflection

Then, from $\triangle A'B'C'$ to $\triangle A''B'C''$, it is a reflection across line $m$. The notation for reflection across line $m$ is $r_{m}$.

Step3: Determine composition order

The composition of transformations is first the rotation and then the reflection. The notation for composition of transformations is read from right - to - left. So the composition is $r_{m}\circ R_{B,90^{\circ}}$.

Answer:

$r_{m}\circ R_{B,90^{\circ}}$