https://file.aiquickdraw.com/mathbot/file/1727230569927bb9g1ox1.jpg

To determine why the scale factor from Polygon A to Polygon B is 2, let's analyze the dimensions of the two polygons shown.

- **Polygon A** has side lengths of 1.5 and 2.5.
- **Polygon B** has corresponding side lengths of 3 and 5.

A scale factor compares the lengths of corresponding sides of two similar polygons. In this case, to find the scale factor, we divide the length of a side in Polygon B by the length of the corresponding side in Polygon A.

- For the side with length 5 in Polygon B and the corresponding side with length 2.5 in Polygon A, the ratio is:
  \[
  \frac{5}{2.5} = 2
  \]
- For the side with length 3 in Polygon B and the corresponding side with length 1.5 in Polygon A, the ratio is:
  \[
  \frac{3}{1.5} = 2
  \]

Since both corresponding sides give a scale factor of 2, the polygons are scaled versions of each other with a scale factor of 2.

### Conclusion:
The scale factor that takes Polygon A to Polygon B is 2 because the lengths of corresponding sides in Polygon B are twice the lengths of the corresponding sides in Polygon A.

Would you like more details or have any further questions?

Here are 5 related questions you could explore:
1. How do you verify that two polygons are similar?
2. Can the scale factor be applied to angles as well as sides?
3. How do you calculate the area of Polygon B using the scale factor?
4. What happens to the perimeter of Polygon B in comparison to Polygon A?
5. How do you apply a scale factor to polygons in coordinate geometry?

**Tip**: Always compare corresponding sides and check if the ratios are consistent to determine the scale factor.

Understand why the scale factor between two similar polygons, A and B, is 2. Learn how to use the scale factor formula by comparing corresponding side lengths to confirm the ratio. Suitable for Grades 6-8.

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