Question

which rigid transformation would map δabc to δabf?
○ a rotation about point a
○ a reflection across the line containing $overline{cb}$
○ a reflection across the line containing $overline{ba}$
○ a rotation about point b

Explanation:

To determine the rigid transformation mapping $\triangle ABC$ to $\triangle ABF$, we analyze the diagram. A rigid transformation preserves shape and size. Looking at the triangles, $\overline{BA}$ is a common side. Reflecting across the line containing $\overline{BA}$ would map point $C$ to $F$ (since the markings show congruent sides/angles), aligning $\triangle ABC$ with $\triangle ABF$. Rotation about $A$ or $B$ doesn't fit as well, and reflection across $\overline{CB}$ is incorrect.

Answer:

C. a reflection across the line containing $\overline{BA}$