Question

which rigid transformation would map △ mzk to △ qzk? a rotation about point k a reflection across the line containing \\(\overline{mz}\\) a reflection across the line containing \\(\overline{zk}\\) a rotation about point z

Explanation:

A rigid transformation preserves shape and size. Looking at $\triangle MZK$ and $\triangle QZK$, the line $ZK$ is common to both triangles, and $ZK$ is perpendicular to $MQ$ at $Z$. Reflecting $\triangle MZK$ across the line containing $ZK$ will flip the triangle over this line, mapping point $M$ to point $Q$, while points $Z$ and $K$ remain fixed, thus mapping $\triangle MZK$ to $\triangle QZK$.

Answer:

a reflection across the line containing $\overline{ZK}$