Question

which of the following sequences of transformations maps △xyz onto △abc? sequence a a translation 2 units to the right and 10 units up, then a reflection over the line \overleftrightarrow{ac}. sequence b a translation 6 units to the right and 6 units up, then a 180° rotation about point b. choose 1 answer: \text{a} only sequence a \text{b} only sequence b \text{c} both

Explanation:

Step1: Analyze Sequence A

Translate \( \triangle XYZ \) 2 units right and 10 units up. Then reflect over \( \overleftrightarrow{AC} \). This aligns \( \triangle XYZ \) to \( \triangle ABC \) as translations and reflections preserve shape/size, matching the triangles.

Step2: Analyze Sequence B

Translate \( \triangle XYZ \) 6 units right and 6 units up. Then rotate \( 180^\circ \) about \( B \). A \( 180^\circ \) rotation and translation also preserve congruence, mapping \( \triangle XYZ \) to \( \triangle ABC \).

Answer:

C. Both