Asegment with endpoints (2, -1) and (4,2) is dilated to the image segment with endpoints (4, -2) and (8,4). what is the scale factor for dilation?

Hey there! A scale factor means the amount that the image is growing or shrinking compared to an original image. If you used some graph paper to make a point at (2,-1) and (4,2) and them made another image marked at points (4,-2) and (8,4), you would see that the image is twice as big. This means the scale factor is 200% or 2 times as big.
Hope this helps. :)