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?

• a reflection across the line containing \\( \overline{hj} \\)
• a rotation about point \\( k \\)
• a rotation about point \\( h \\)
• a reflection across the line containing \\( \overline{hk} \\)

Explanation:

Step1: Analyze the properties of rigid transformations

Rigid transformations (translation, rotation, reflection) preserve the shape and size of the figure. Translation moves the figure without rotation or reflection.

Step2: Consider the effect of rotation

Since vertex \(H\) is translated to \(L\), to map \(\triangle HJK\) to \(\triangle LMN\) (given the SAS congruence - side - angle - side, where the angle is at \(H\) and \(L\) after translation), a rotation about point \(H\) (which is now at \(L\) after translation) will align the other sides and angles of the triangle. A reflection across a line (either \(HJ\) or \(HK\)) would change the orientation in a way that is not consistent with the given congruence setup. Rotation about \(K\) is not relevant as the key vertex for alignment (after translation) is \(H\) (now at \(L\)).

Answer:

a rotation about point \(H\)