How do we graph dilations?

Dilations are a type of transformation that causes. An image to stretch or shrink in proportion to it's original size. To know which to do you use a scale factor that tells you how much the original has grown or shrink. For example the point (6,3) and the scale factor is 3 shown as D3. You times the (x,y) by three. Which would end with a point (18,9). A problem would be the three points A (1,2) B (3,2) andC (3,1). A' is (8, 16). What is the scale factor?