AB can be represented as (c-a,d-b)
since C divides AB in the ratio p:q,
C = A+AC
Thanks heaps badgerigar! I notice how you switched the ordered pairs from coordinate points into length units, that was smart.
This probably isn't that important seeing as the main aim has been achieved, but for all purposes shouldn't AB be (|c-a|, |d-b|)
So the final coordinates become
Thanks again
No. If c-a is negative that means that point B is left of point A. taking the absolute value sign will have you adding a positive value to the x value of A, since \frac{p}{p+q} is positive. This will put C to the right of A, so not between A and B.
If you want to think about an example try A=(3,0) B=(0,0) and the ratio 1:2