Question

two rigid transformations are used to map \\( \triangle hjk \\) to \\( \triangle lmn \\). the first is a translation of vertex \\( h \\) to vertex \\( l \\). what is the second transformation? \\( \bigcirc \\) a reflection across the line containing \\( \overline{hk} \\) \\( \bigcirc \\) a rotation about point \\( h \\) \\( \bigcirc \\) a reflection across the line containing \\( \overline{hj} \\) \\( \bigcirc \\) a rotation about point \\( k \\)

Explanation:

Rigid transformations include translation, rotation, and reflection. After translating vertex \(H\) to vertex \(L\), we need to check the orientation of the triangles. A rotation about a point (not about \(H\) as \(H\) has been translated to \(L\)) can align the triangles. Since the first transformation is a translation of \(H\) to \(L\), the second transformation is a rotation about point \(K\) (because after translation, rotating about \(K\) will map the other vertices correctly). A reflection across a line containing a side of \(\triangle HJK\) (like \(HK\) or \(HJ\)) would change the orientation in a way that is not consistent with the mapping of the triangles shown (if we consider the congruence and the order of vertices after translation). A rotation about \(H\) is incorrect as \(H\) is moved to \(L\) in the first step.

Answer:

a rotation about point \(K\)