Question

two rigid transformations are used to map △jkl to △mnq. the first is a translation of vertex l to vertex q. what is the second transformation? a reflection across the line containing lk a reflection across the line containing jk a rotation about point l a rotation about point k

Explanation:

After translating vertex L to vertex Q, to map △JKL to △MNQ, we observe the orientation of the triangles. A reflection across the line containing $\overline{LK}$ will align the two triangles as the angles and side - lengths match up correctly after the translation. A reflection across $\overline{JK}$ would not align them properly. Rotations about point L or K would not achieve the correct mapping as rotations change the orientation in a circular fashion around a point and won't align the triangles as needed after the translation.

Answer:

a reflection across the line containing $\overline{LK}$