Question

Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?

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 diagram, so I can’t pick the correct choice directly. Here’s how you can decide which composition is correct:

1. Compare sizes to get the scale factor:
- Measure one pair of corresponding side lengths (e.g., AB and A′B′).
- If length(A′B′)/length(AB) < 1 the dilation has scale factor less than 1 (shrink). If > 1 it’s greater than 1 (enlarge).

2. Check whether the polygon was mirrored (reflection) or not:
- Look at the vertex order around the polygon. If ABCD is listed clockwise and A′B′C′D′ is counterclockwise (or vice versa), the orientation was reversed → a reflection is involved.
- If the orientation (handedness) is the same, there is no reflection. (A translation or rotation preserves orientation.)

3. Decide between reflection and translation:
- If orientation was reversed → choose the option with “and then a reflection.”
- If orientation was preserved and the polygon was just moved → choose the option with “and then a translation.”

So:
- Shrunk + same orientation → “dilation with scale factor less than 1 and then a translation.”
- Shrunk + reversed orientation → “dilation with scale factor less than 1 and then a reflection.”
- Enlarged + same orientation → “dilation with scale factor greater than 1 and then a translation.”
- Enlarged + reversed orientation → “dilation with scale factor greater than 1 and then a reflection.”

If you can upload the figure or give coordinates/side lengths and vertex order, I’ll pick the exact option for you.