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maths gcse help higher URGENT

Point C lies on the segment AB. Find the coordinates of C given that:
A=(3,-3)
B=(6,6)
AC:CB=1:2

I understand that you need to find the difference of x first. So 6-3=3. Then find the difference of y, so 6--3=9. Then work out 1/3 of each which is 1,3. Then add this onto the coordinate A, giving the coordinate of C which is (4,0). My question is why can't you do 3-6 for the x difference and -3-6 for the y difference. I know it gives a different answer but how are you meant to know which way round to do it? Also why is it 1/3 can't you do 2/3. I am basically confused which way round you minus the coordinates and why, and the fractions and everything, because I know for gradients it doesn't matter which one is x1 and which is x2 (or which is y1 or y2) as they give the same answer either way, but how about here? Thanks I would appreciate if you could help me quickly :smile: