Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.

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

1 answer

To determine the second transformation that maps triangle HJK to triangle LMN, we need to consider the properties of congruent triangles and the transformations described.

  1. The first transformation is a translation of vertex H to vertex L. This means that point H moves directly to point L.
  2. Triangle LMN is the result of rotating triangle HJK about point H to form triangle LNM, meaning we also need to consider how the other vertices A and B (the remaining vertices after the translation) map.

Since the two triangles are congruent, after translating H to L, we look for a transformation that will correctly align the remaining vertices.

If we assume:

  • A translation moves H to L,
  • Then we need a transformation that appropriately aligns J and K to M and N respectively.

Given that triangle LMN is "higher" than triangle HJK, this suggests that there may be a vertical reflection involved.

Among the options provided:

  1. A reflection across the line containing HK
  2. A rotation about point H
  3. A reflection across the line containing HJ
  4. A rotation about point K

The most reasonable choice that ensures the new triangle LMN retains the orientation would be to perform a reflection across the line containing HK after the translation. This aligns J and K to M and N appropriately.

Thus, the second transformation is:

a reflection across the line containing HK.