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:

Step1: Analyze translation

Translation moves a figure without rotation or reflection. We need to move a corresponding vertex. Since \(K\) and \(N\) are corresponding vertices (by side - length and angle markings in congruent triangles), we first translate \(K\) to \(N\).

Step2: Analyze reflection

After translating \(K\) to \(N\), we need to reflect. The side \(JK\) (in \(\triangle HJK\)) and \(MN\) (in \(\triangle LMN\)) are corresponding. Reflecting across the line containing \(\overline{JK}\) (after translating \(K\) to \(N\)) will map \(\triangle HJK\) to \(\triangle LMN\) because reflection is a rigid transformation that flips a figure over a line.

Answer:

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