Geometry, I need help

Question

A dilation has center (0, 0). Find the image of each point for the given scale factor. 

C(0,4);D(12)(C)

A. (1/2, 0))

B. (4,0)

C. (0,2)

D. (1/2, 4/1)

Answer 1

I can't tell what the scale factors are from your problem statement, but let's call it k. For a given point (x,y), the rule for dilating about the origin is:

dilate by k about (0,0)

(x,y) ------------------------------> (kx,ky)

where (kx,ky) is the image of (x,y) after the dilation. For example, if k = 3 and (x,y) = (1/2, -2), the dilated point would be ( 3·(1/2), 3·(-2) ) = (3/2,-6).