Question

which rigid transformation would map △mzk to △qzk?
a rotation about point k
a reflection across the line containing mz
a reflection across the line containing zk
a rotation about point z

Explanation:

Step1: Analyze rigid - transformations

Rigid transformations include rotations and reflections. We need to check each option for mapping △MZK to △QZK.

Step2: Evaluate rotation options

A rotation about point K or Z will not map △MZK to △QZK as the orientation and position of the triangles relative to these points will not match the required transformation.

Step3: Evaluate reflection options

The line containing $\overline{ZK}$ is the perpendicular bisector of $\overline{MQ}$. Reflecting △MZK across the line containing $\overline{ZK}$ will map point M to point Q, while keeping points Z and K in the same position, thus mapping △MZK to △QZK.

Answer:

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