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 see the picture, so I can't pick the correct choice directly. Tell me the diagram or the coordinates (or upload the figure) and I will pick the right option. Meanwhile, here's how you decide which composition is correct:

1. Determine the scale factor of the dilation:
- Measure a distance from the dilation center to a vertex and the corresponding distance to its image. The scale factor k = (image distance)/(original distance).
- If k < 1 the triangle shrank; if k > 1 it grew.

2. Decide whether a reflection is needed or only a translation:
- Check the orientation (order) of the vertices. If LMN and L'M'N' are listed in the same cyclic order (both clockwise or both counterclockwise), orientation is preserved → no reflection needed (use translation if there is any remaining displacement).
- If the vertex order is reversed (one clockwise, the other counterclockwise), orientation is reversed → a reflection is required.

3. Match to the choices:
- k < 1 and orientation reversed → "dilation with scale factor less than 1 and then a reflection."
- k < 1 and orientation preserved → "dilation with scale factor less than 1 and then a translation."
- k > 1 and orientation reversed → "dilation with scale factor greater than 1 and then a reflection."
- k > 1 and orientation preserved → "dilation with scale factor greater than 1 and then a translation."

If you post the figure or coordinates (e.g., L( ), M( ), N( ) and L'( ), M'( ), N'( )), I’ll compute k and the orientation and give the exact choice.