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

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.

Step2: Analyze rotation

After translation, we rotate about the translated vertex to align the sides. We want to align the sides of the two triangles. If we translate $K$ to $N$, then rotating about $K$ (now at the position of $N$) can be used to align $\overline{HK}$ with the line containing $\overline{LN}$.

Answer:

Translate K to N and rotate about K until $\overline{HK}$ lies on the line containing $\overline{LN}$.