Question

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

Explanation:

Step1: Analyze the triangles

We have two triangles \(\triangle WXY\) and \(\triangle MNQ\). We know that when we translate vertex \(W\) to vertex \(M\), we need to find the line of reflection.

Step2: Check the corresponding sides and angles

In \(\triangle WXY\), side \(WX = 18\mathrm{cm}\) and in \(\triangle MNQ\), side \(MN=18\mathrm{cm}\). Side \(WY = 30\mathrm{cm}\) and \(MQ = 30\mathrm{cm}\). The angle between \(WX\) and \(WY\) in \(\triangle WXY\) corresponds to the angle between \(MN\) and \(MQ\) in \(\triangle MNQ\). If we translate \(W\) to \(M\), the line of reflection should be the line that maps the remaining parts of the triangle. Since \(WY\) and \(MQ\) are corresponding sides of length \(30\mathrm{cm}\), reflecting across the line containing \(\overline{WY}\) (after translation of \(W\) to \(M\)) will map \(\triangle WXY\) to \(\triangle MNQ\)

Answer:

\(\overline{WY}\)