two rigid transformations are used to map $\triangle jkl$ to $\triangle mnq$. the first is a translation of…

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?\n○ a reflection across the line containing $overline{lk}$\n○ a reflection across the line containing $overline{jk}$\n○ a rotation about point l\n○ a rotation about point k

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?\n○ a reflection across the line containing $overline{lk}$\n○ a reflection across the line containing $overline{jk}$\n○ a rotation about point l\n○ a rotation about point k

Answer

Brief Explanations:

First, after translating vertex L to vertex Q, we align the two triangles such that L and Q coincide. Observing the orientation of the sides: $\overline{LK}$ corresponds to $\overline{QN}$, and $\overline{LJ}$ corresponds to $\overline{QM}$. A reflection across the line containing $\overline{LK}$ (which becomes the line containing $\overline{QN}$ after translation) will map the translated $\triangle JKL$ to $\triangle MNQ$, as it flips the triangle to match the orientation of the target figure. Other options do not result in the correct mapping: reflecting across $\overline{JK}$ would not align the vertices, and rotations about L or K would preserve the original orientation which does not match $\triangle MNQ$.

Answer:

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