Question

If ΔMNL is rotated 180° about point N, which additional transformation could determine if ΔONP and ΔMNL are similar by the AA similarity postulate?

Segments OM and LP intersect at point N; triangles are formed by points LNM and ONP; line k intersects with both triangles at point N.

Reflect ONP over line k.
Reflect M'N'L' over line k.
Dilate ONP from point N by a scale factor of segment NP over segment NL.
Dilate M'N'L' from point N by a scale factor of segment NP over segment NL

Answer 1

The answer is D because you need to make it smaller by dilation. This leaves the last two options. D makes the most sense.

Answer 2

Dilate M'N'L' from point N by a scale factor of segment NP over segment NL

Explanation:

Multiplying the length of N'L' by the factor NP/NL will give it the length of NP, making the dilated version of ΔM'N'L' congruent to ΔONP. This is apparently your goal.

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Reflection over line k doesn't seem to do anything useful, and the other offered dilation is by the wrong factor. You want to ...

dilate M'N'L' from point N by a scale factor of segment NP over segment NL.