maths help URGENT GCSE HIGHER

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:

Reply 1

tonyiptony

I'd say draw a picture to see roughly where A, B, and C are first.

Have you learned the concept of vectors? It would make more sense how your method works if you know a bit about vectors. If not, have you come across a formula that deals with this problem?

Moral of the story: (i) draw a picture first wherever possible; (ii) don't use a method that is confusing to you.