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 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

A 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. Translating a key vertex is the first step.

Step2: Analyze reflection

After translation, a reflection flips the figure over a line. We need to find a line of reflection that will map the remaining parts of the triangle correctly.
When we translate $K$ to $N$, we then need to reflect across a line that will align the other vertices. Reflecting across the line containing $\overline{JK}$ will map the triangle $\triangle HJK$ to $\triangle LMN$.

Answer:

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