Question

Draw a rectangle on a coordinate plane. Choose a scale factor of 2,3,4, or 5, and then dilate the rectangle. How many times greater is the area of the image than the area of the original triangle? many times greater is the area of the image than the area of the original triangle?

Answer 1

If you have a rectangle that is 2 by 2 and you dilate it by 2, the sides are now 4 x 4. So:
If you dilate it by a factor of 2, the area is 2^2 (4) times as great
A factor of 3 would have an area of 9 times as much.

Conclusion: square the scale factor to get how much greater the area would be.