# Analytic geometry - finding point by intersect lin

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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

• Analytic geometry - finding point by intersect lin -

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
y-k = -h/k (x-h)

The altitude from C to AB is
y-n = -m/n (x-m)

solve for x and y.

Trilinear coordinates are much cleaner, but less well known.

• Analytic geometry - finding point by intersect lin -

thanks a bunch

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