Question

how can a translation and a reflection be used to map △hjk to △lmn? translate k to n and reflect across the line containing $overline{hj}$. translate k to l and reflect across the line containing $overline{hj}$. translate h to l and reflect across the line containing $overline{jk}$. translate k to n and reflect across the line containing $overline{jk}$.

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation or reflection. To map $\triangle HJK$ to $\triangle LMN$, we first need to align one - to - one corresponding vertices. We note that vertex $K$ should be translated to vertex $N$ as they are corresponding vertices.

Step2: Analyze reflection

After translating $K$ to $N$, we need to reflect the triangle to match the orientation. The line of reflection should be such that the other vertices also match. Reflecting across the line containing $\overline{HJ}$ will map the remaining vertices of $\triangle HJK$ to the vertices of $\triangle LMN$.

Answer:

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