Question

two rigid transformations are used to map δhjk to δlmn. the first is a translation of vertex h to vertex l. what is the second transformation?
○ a reflection across the line containing $overline{hk}$
○ a rotation about point h
○ a reflection across the line containing $overline{hj}$
○ a rotation about point k

Explanation:

After translating vertex \( H \) to \( L \), we need to align the triangles. A rotation about point \( H \) (now \( L \)) would adjust the orientation to match \( \triangle LMN \). Let's analyze the options:

• Reflection across \( \overline{HK} \): Doesn't align the triangles correctly as per the diagram's congruency and orientation.
• Rotation about point \( H \): After translating \( H \) to \( L \), rotating about \( H \) (now \( L \)) can map the remaining vertices.
• Reflection across \( \overline{HJ} \): Incorrect orientation adjustment.
• Rotation about point \( K \): Doesn't align with the translation's result.

So the correct transformation is a rotation about point \( H \).

Answer:

a rotation about point H