Question

how can $\triangle wxy$ be mapped to $\triangle mnq$?
translate vertex w to vertex m, then reflect across the line containing _____________.
$\overline{wx}$
$\overline{wy}$
$\overline{xy}$
$\overline{mq}$

Explanation:

Step1: Identify corresponding sides

In $\triangle WXY$, sides: $WY=30\mathrm{cm}$, $WX=18\mathrm{cm}$. In $\triangle MNQ$, sides: $MQ=30\mathrm{cm}$, $MN=18\mathrm{cm}$. After translating $W$ to $M$, $WX$ aligns with $MN$, $WY$ aligns with $MQ$.

Step2: Determine reflection line

To map $\triangle WXY$ to $\triangle MNQ$ after translation, we need to reflect across the line that preserves the correspondence of the adjacent sides to the common vertex. The line containing the side that matches the shared vertex's aligned pair is $\overline{WX}$ (which becomes $\overline{MN}$ after translation). Reflecting across this line swaps the positions of the other vertices to match $\triangle MNQ$.

Answer:

$\boldsymbol{\overline{WX}}$