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:

To determine the rigid transformation mapping \( \triangle MZK \) to \( \triangle QZK \), we analyze the diagram:

• \( Z \) is the midpoint of \( MQ \), and \( KZ \perp MQ \) (right angle at \( Z \)).
• A rotation about point \( Z \): Rotating \( \triangle MZK \) 180° (or 180° - equivalent rotation) about \( Z \) would map \( M \) to \( Q \) (since \( ZM = ZQ \)) and keep \( K \) and \( Z \) fixed, aligning \( \triangle MZK \) with \( \triangle QZK \).
• Other options: Rotation about \( K \) or reflection across \( MZ \)/\( ZK \) do not align the triangles as \( Z \) is the symmetry center here.

Answer:

D. a rotation about point \( Z \)