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 $overline{hj}$. translate k to n and reflect across the line containing $overline{jk}$. translate h to l and reflect across the line containing $overline{jk}$. translate k to l and reflect across the line containing $overline{hj}$.

Explanation:

Step1: Analyze translation

To map $\triangle HJK$ to $\triangle LMN$, we first need to align one - to - one corresponding vertices. Translating a point helps in moving the triangle to a position where it can be further transformed to match the other triangle. We want to match corresponding vertices. Translating $K$ to $N$ is a good start 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 of $\triangle LMN$. Reflecting across the line containing $\overline{JK}$ will align the two triangles correctly as the shape and orientation will match after this reflection following the translation of $K$ to $N$.

Answer:

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