Question

Which composition of similarity transformations maps TriangleLMN to TriangleL'M'N'?

a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation

Answer 1

I don't have the picture or coordinates, so I can't pick the correct option yet. Here is how you decide from the diagram (so you can pick one of the four choices):

1. Identify corresponding vertices (L → L', M → M', N → N').
2. Find the scale factor: compute one corresponding side length ratio, e.g. s = L'M' / LM (or M'N' / MN).
- If s < 1 the dilation is a shrink (scale factor less than 1).
- If s > 1 it is an enlargement (scale factor greater than 1).
3. Check orientation (whether the triangle has been mirrored): compute the sign of the triangle area (or the orientation of the ordered triple). For points A,B,C the signed area (up to factor 1/2) is
det = (Bx−Ax)(Cy−Ay) − (By−Ay)(Cx−Ax).
- If sign(det) for L,M,N and for L',M',N' are the same, orientation is preserved → no reflection (so a translation or rotation after dilation).
- If the signs are opposite, orientation is reversed → a reflection is involved.
4. Since your answer choices only allow “reflection” or “translation” after the dilation, choose:
- “dilation with scale < 1 and then a reflection” if s < 1 and orientation is reversed.
- “dilation with scale < 1 and then a translation” if s < 1 and orientation is preserved.
- “dilation with scale > 1 and then a reflection” if s > 1 and orientation is reversed.
- “dilation with scale > 1 and then a translation” if s > 1 and orientation is preserved.

If you post the diagram or the coordinates of L,M,N and L',M',N', I’ll compute and tell you which option is correct.