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

To map $\triangle HJK$ to $\triangle LMN$, first, we need to match a corresponding vertex. Translating a vertex of $\triangle HJK$ to the corresponding vertex of $\triangle LMN$ is the first - step. We want to align the triangles in position. Translating $K$ to $N$ makes sense as $K$ and $N$ are corresponding vertices.

Step2: Analyze reflection

After translating $K$ to $N$, we need to reflect the triangle to match the orientation. Reflecting across the line containing $\overline{JK}$ will map the remaining vertices of $\triangle HJK$ to the corresponding vertices of $\triangle LMN$.

Answer:

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