Question

two rigid transformations are used to map \\(\delta jkl\\) to \\(\delta 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:

Analyze the first transformation

Using the Rigid Transformations and Congruence Mapping knowledge points

• The first transformation is a translation mapping vertex \(L\) to vertex \(Q\).
• After this translation, the image of \(\triangle JKL\), which we can denote as \(\triangle J'K'L'\), has vertex \(L'\) coinciding with vertex \(Q\).

Determine the orientation and second transformation

Using the Composition of Transformations knowledge point

• In \(\triangle JKL\), the side \(\overline{JL}\) has a single tick mark, and the angle at \(L\) has a double arc.
• In \(\triangle MNQ\), the side \(\overline{MQ}\) has a single tick mark, and the angle at \(Q\) has a double arc.
• Since \(L'\) is at \(Q\), the segment \(\overline{J'L'}\) must align with \(\overline{MQ}\).
• To map the rest of the translated triangle \(\triangle J'K'L'\) onto \(\triangle MNQ\), we must reflect it across the line containing the aligned segment \(\overline{J'L'}\), which corresponds to the line containing \(\overline{LK}\) in the original triangle's relative orientation.
• Therefore, the second transformation is a reflection across the line containing \(\overline{LK}\).

Answer:

• a reflection across the line containing \(\overline{LK}\) (Correct answer)
• a reflection across the line containing \(\overline{JK}\)
• a rotation about point L
• a rotation about point K