Question

which rule describes the composition of transformations that maps △abc to △abc?
options (in boxes):
$r_{b, 90^circ} \circ r_m$
$r_m \circ r_{b, 270^circ}$
$r_{b, 270^circ} \circ r_m$
$r_m \circ r_{b, 90^circ}$
(diagram shows △abc, line ( m ), △abc (after reflection/rotation), and △abc )

Explanation:

Step1: Identify transformations

Key transformations: reflection over line \( m \) (\( r_m \)) and rotation about \( B' \) (\( R_{B'} \)).

Step2: Determine order and angle

First rotate \( \triangle ABC \) 270° about \( B' \), then reflect over \( m \). Composition: \( r_m \circ R_{B', 270^\circ} \).

Answer:

\( r_m \circ R_{B', 270^\circ} \)