Question

how can a translation and a reflection be used to map δhjk to δlmn?
○ translate k to n and reflect across the line containing hj.
○ translate k to n and reflect across the line containing jk.
○ translate h to l and reflect across the line containing jk.
○ translate k to l and reflect across the line containing hj.

Explanation:

To map \(\triangle HJK\) to \(\triangle LMN\), we analyze the congruent sides and angles. First, translating \(K\) to \(N\) aligns the vertical segments (since \(JK\) and \(MN\) are vertical with equal length). Then, reflecting across the line containing \(JK\) (which is vertical) will map the remaining points correctly, as the angles and side lengths match after this translation - reflection combination. Other options either translate incorrect points (like \(H\) to \(L\) or \(K\) to \(L\)) or reflect across the wrong line, which would not align the triangles properly.

Answer:

B. Translate \(K\) to \(N\) and reflect across the line containing \(\overline{JK}\)