Question

how can \\( \triangle wxy \\) be mapped to \\( \triangle mnq \\)?
translate vertex \\( w \\) to vertex \\( m \\), then reflect across
the line containing
\\( \overline { w x } \\)
\\( \overline { w y } \\)
\\( \overline { x y } \\)
\\( \overline { m q } \\)

Explanation:

When translating vertex \(W\) to vertex \(M\), we need to find the line of reflection such that the two triangles \(\triangle WXY\) and \(\triangle MNQ\) are congruent. By analyzing the side - angle - side (SAS) congruence ( \(WX = MN=18\mathrm{cm}\), \(WY = MQ = 30\mathrm{cm}\), and the included angles), we observe that reflecting across the line containing \(\overline{WY}\) (after translation of \(W\) to \(M\)) will map \(\triangle WXY\) to \(\triangle MNQ\).

Answer:

\(\overline{WY}\)