Question

two rigid transformations are used to map \\( \triangle jkl \\) to \\( \triangle mnq \\). the first is a translation of vertex \\( l \\) to vertex \\( q \\). what is the second transformation? a reflection across the line containing \\( \overline{lk} \\) a reflection across the line containing \\( \overline{jk} \\) a rotation about point \\( l \\) a rotation about point \\( k \\)

Explanation:

• Rigid transformations include translations, rotations, and reflections.
• After translating vertex \(L\) to vertex \(Q\), we need to check the orientation of the triangles.
• If we consider the congruent triangles \(\triangle JKL\) and \(\triangle MNQ\), a rotation about point \(K\) (which is a common - point after translation of \(L\) to \(Q\) in terms of the transformation sequence) can map \(\triangle JKL\) to \(\triangle MNQ\).
• A reflection across the line containing \(\overline{LK}\) or \(\overline{JK}\) would change the orientation in a way that is not consistent with the given mapping (by visual inspection of the angle markings and side - length markings, if we assume the triangles are congruent as per rigid - transformation mapping). A rotation about point \(L\) is not valid because \(L\) is translated to \(Q\) first.

Answer:

a rotation about point \(K\)