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.
- The first transformation is a translation of vertex H to vertex L. This means that point H moves directly to point L.
- 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:
- A reflection across the line containing HK
- A rotation about point H
- A reflection across the line containing HJ
- 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.