Question

Two rigid transformations are used to map ΔHJK to ΔLMN. The first is a translation of vertex H to vertex L. What is the second transformation?

a reflection across the line containing HK
a rotation about point H
a reflection across the line containing HJ
a rotation about point K

Answer 1

I don’t have the diagram, so I can’t pick the correct option yet. Could you either upload the diagram or give coordinates/relative positions of H,J,K and L,M,N?

If you want to decide it yourself, here’s a quick procedure:

1. Apply the translation that sends H to L to the whole triangle. Call the images J' and K' of J and K.
2. Check where J' and K' end up relative to M and N:
- If J' = M and K' = N then the translation alone did it (no second transformation needed).
- If J' and K' are the mirror images of M and N across a line through L, then the second transformation is a reflection about that line. Since the choices give lines through H (which after the translation become lines through L), test reflection across the line through L and K' (originally HK) and the line through L and J' (originally HJ) to see which sends J'→M and K'→N.
- If J' and K' are rotated around L (the image of H) to match M and N, then the second transformation is a rotation about H (i.e., about L after the translation). If a rotation about K is listed, that would require the center to be K (or its image), so test that too.

How to test reflections/rotations quickly:
- Reflection test: reflect J' across the candidate line; see if you get M (and check K'→N).
- Rotation test: compute the angle from L to J' and from L to M; if those angles differ by the same amount (and distance LJ' = LM), then a rotation about L by that amount maps J' to M.

If you send the diagram or coordinates I’ll apply this and pick the correct choice.