Question

how can △wxy be mapped to △mnq? translate vertex w to vertex m, then reflect across the line containing xy wy mq wx

Explanation:

Step1: Analyze the translation

Translate vertex \(W\) to vertex \(M\). This moves the triangle so that one vertex is in the correct position.

Step2: Analyze the reflection

After translating \(W\) to \(M\), we need to reflect across the line that will map the other vertices correctly. Looking at the triangles \(\triangle WXY\) and \(\triangle MNQ\), when \(W\) is translated to \(M\), the line containing \(WX\) (after translation, the corresponding side - like segment) will be the line of reflection. Because the sides \(WX = MN=18\mathrm{cm}\), \(WY = MQ = 30\mathrm{cm}\) and the included angles \(\angle W=\angle M\). Reflecting across the line containing \(WX\) (after translation) will map \(Y\) to \(Q\) and \(X\) to \(N\)

Answer:

\(WX\)