Atriangle has a vertex coordinates of (3,4), (2,6) and (1,1). after a dilation from the origin, the dilated image has vertex coordinates of (15,20), (10,30) and (5,5). what is the scale factor of the dilated triangle?

To find the dilation factor, divide the new coordinate by the old coordinate.

take (3,4) and (15, 20) for instance; 15/3 = 5 and 20/5 = 5 as well. to make sure, check this for the remaining coordinates as well and you'll get 5 for all of them, so the scale factor is 5.