Question

two rigid transformations are used to map △hjk to △lmn. 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:

Step1: Analyze translation effect

After translating vertex \(H\) to vertex \(L\), we need to align the other vertices. A rotation about point \(K\) (while keeping \(K\) fixed after translation - since translation moves all points of the figure) can be used to map \(\triangle HJK\) to \(\triangle LMN\) as rigid - transformations (translation and rotation) preserve shape and size.
A reflection across a line (like \(\overline{HK}\) or \(\overline{HJ}\)) would change the orientation in a way that is not consistent with the given figure (after translation, rotation about a point is more appropriate). A rotation about point \(H\) is not useful as \(H\) has been translated to \(L\).

Answer:

a rotation about point \(K\)