Hi, I have the following exercise and I am kind of stuck in the last bit now... There exercise says
"Consider the simple right-angled triangle ABC in the diagram above. The points P, Q, R divide the sides of the triangle in the ratios indicated. Find the coordinates of the points P, Q, R in terms of s, t, u. (Q having 1 and t on each side is only the ratio, it doesn't mean that the length between Q and C is 1)
Well...so far I have Q=(0, t/(t+1)) and R=(1/(1+u), 0)... How do I get P though? Thanks a lot!
OK... I am stuck again . How do you solve these parametric equations? (they need to be in terms of t and u). I'd just like to have a tip so that I can work on it myself and learn...
So, I got for BQ:
(x, y)=(1,0)+m(-1, t/(1+t))
and for CR I got:
(x, y)=(0,1)+n(1/(1+u), -1)
I know I have to equate the x and y, but I still can't get rid of m and n...
So I got
1-m=n/(1+u) and mt/(t+1)=1-n
So I substituted n=1+u-m-mu into
mt/(t+1)=1-n, but I get mt=m+mu-u-tu+mut+mt
How am I supposed to get rid of n and m then? :-/