Question

how can a translation and a rotation be used to map △hjk to △lmn? translate h to l and rotate about h until hk lies on the line containing lm. translate k to m and rotate about k until hk lies on the line containing lm. translate k to n and rotate about k until hk lies on the line containing ln. translate h to n and rotate about h until hk lies on the line containing ln.

Explanation:

Step1: Analyze translation concept

Translation moves a figure without rotation. To map $\triangle HJK$ to $\triangle LMN$, we first need to match a corresponding vertex.

Step2: Analyze rotation concept

Rotation is turning a figure around a point. After translation, we rotate to align the sides.
To map $\triangle HJK$ to $\triangle LMN$, we should translate a vertex of $\triangle HJK$ to the corresponding vertex of $\triangle LMN$. Translating $H$ to $L$ first will align one vertex. Then rotating about $H$ (the translated - vertex) until $\overline{HK}$ lies on the line containing $\overline{LM}$ will help in mapping the triangles.

Answer:

Translate $H$ to $L$ and rotate about $H$ until $\overline{HK}$ lies on the line containing $\overline{LM}$.