Question

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

Explanation:

First, after translating vertex L to Q, we look at the orientation of the triangles and the position of corresponding angles. The marked angles at L/Q and J/M show that a reflection would flip the triangle's orientation, but the angle positions match a rotation about point L (now mapped to Q). A reflection across LK or JK would not align the corresponding vertices and angles correctly as seen in the diagram, while a rotation about point L (after translation, L is Q) maps the remaining vertices to match △MNQ.

Answer:

a rotation about point L