Question

4520va v. geometry sem a geometry compositions which rule describes the composition of transformations that maps △abc to △abc? r_{b, 270°} ∘ r_m r_m ∘ r_{b, 90°} r_m ∘ r_{b, 270°} r_{b, 90°} ∘ r_m

Explanation:

Step1: Analyze the transformation from △ABC to △A'B'C'

First, observe that △ABC is rotated 90 - degrees counter - clockwise about point B' to get △A'B'C'. The rotation notation is \(R_{B',90^{\circ}}\).

Step2: Analyze the transformation from △A'B'C' to △A''B'C''

Then, △A'B'C' is reflected across line m. The reflection notation is \(r_m\).

Step3: Determine the composition of transformations

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:

\(r_m\circ R_{B',90^{\circ}}\)