Question

A point at (20, 15) maps on to a point at (4,3). If the dilation occurred centered at the origin, what is the scale factor of that dilation?

Answer 1

You have that the point (20,15) is a dilation of the point (4,3).

In order to determine the scale factor of dilation, you consider that when a point (x,y) is dilated by a factor k, the new point is given by:

(x,y) => (kx , ky) where (kx,ky) is the dilated point

that is, each new coordinate is:

x'= kx

y'= ky

You can solve for k in one of the previous equation, replace the values of the coordinates and obtain the value of k, just as follow:

k = x'/x = 20/4 = 5

k = y'/y = 15/3 = 5

Hence, the scale factor of dilation is k = 5