Question

two rigid transformations are used to map △abc to △xyz. the first is a translation of vertex a to vertex x. what is the second transformation?
options:
a reflection across the line containing (overline{ac})
a reflection across the line containing (overline{ab})
a rotation about point b
a rotation about point a

Explanation:

Step1: Analyze the first transformation

The first transformation is a translation of vertex \( A \) to vertex \( X \). After translation, we need to align the triangles using a rigid transformation (reflection or rotation) that preserves shape and size.

Step2: Check rotation about point \( A \)

A rotation about point \( A \) can align \( \triangle ABC \) to \( \triangle XYZ \) after translation. Let's verify the congruency: sides \( AC \) and \( XZ \) (marked with two ticks), \( AB \) and \( XY \) (marked with one tick), and angles \( \angle CAB \) and \( \angle ZXY \) (marked with arcs) are congruent. Rotation about \( A \) would map \( AB \) to \( XY \) and \( AC \) to \( XZ \), aligning the triangles. Reflections across \( AC \) or \( AB \) don't fit as the first transformation is translation to \( A \to X \), so rotation about \( A \) is the second transformation.

Answer:

a rotation about point \( A \)