How to dilate by 1/3 using center (0,0)

How to dilate a point:

The distance from the center will change by that scale factor.

Let's try an example.
Suppose we have center (0, 0) and point (3, 6).
If we dilated that by 2, it'd become (6, 12).
If we dilated by 1/3, it'd become (1, 2).

With a center that's not (0, 0):
Suppose we have a center (2, 2) and point (8, 6).
If we dilated that by 2, it'd be (14, 10).
If we dilated by 1/2, it'd be (5, 4).

et cetera.

If you can't figure it out, just plug it into this.
(x, y) is the original point. (a, b) is the center. k is the dilation factor.