Question

two rigid transformations are used to map △abc to △qrs. the first is a translation of vertex b to vertex r. what is the second transformation? ○ a reflection across the line containing ab ○ a rotation about point b ○ a reflection across the line containing cb ○ a rotation about point c

Explanation:

Rigid transformations include translations, rotations, and reflections. After translating vertex \(B\) to vertex \(R\), we need to analyze the orientation of the triangles. A rotation about a point can re - orient the triangle. Since the first transformation is a translation of \(B\) to \(R\), and we want to map \(\triangle ABC\) to \(\triangle QRS\), a rotation about point \(C\) (which is a non - translated vertex in the context of the first translation) can align the two triangles properly. Reflections across lines containing sides of \(\triangle ABC\) (like \(AB\) or \(CB\)) would not be the correct second step after translating \(B\) to \(R\), and a rotation about \(B\) is not appropriate as \(B\) has already been translated.

Answer:

a rotation about point \(C\)