Pre-image point n (6,-3) was dilated to point n(2,-1) what was the scale factor used?

The scale factor is 1/3

Explanation:
Given that the original point is has coordinates (x,y) and that the dilated point has coordinates (x',y'), we can see that:
x' = k * x
y' = k * y
where k is the scale factor

Now, for the given point we have:
original point = (6 , -3)
dilated point = (2 , -1)
Now, applying the above formula, we will find that:
For x-coordinate:
2 = k * 6
k = 2/6
k = 1/3
Check using the y-coordinate:
-1 = k * -3
k = -1 / -3
k = 1/3

From the above, we can confirm that:
k = 1/3

Hope this helps :)