Analytic geometry  finding point by intersect lin
posted by Knights on .
I have a triangle ABC. The slope of AB is 1/ab, the slope of AC is 1/ac, and the slope of BC is 1/ac. My question is, I have 3 lines: Altitude from A to BC, altitude from B to AC, and altitude from C to AB. I know their slope because it is just 1/slope. But I want to know the coordinates of where they intersect. Could someone help me? thanks

The details get a bit messy, but you can place A=(0,0) B=(h,k) C=(m,n)
Then the altitude from B to AC is
yk = h/k (xh)
The altitude from C to AB is
yn = m/n (xm)
solve for x and y.
Trilinear coordinates are much cleaner, but less well known. 
thanks a bunch