posted by Anonymous .
Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0
A rather lengthy problem
I will describe the steps
1. Find the vertices of the triangle A, B, and C by solving pairs of equations.
2. Find the slope of line AB. The slope of the perpendicular form C to line AB will be the negative reciprocal of the slope of AB.
You now have the slope of that altitude and a point on it, namely point C
3 . Find the equation of the altitude from C to AB using the form y = mx + b
4. Repeat the procedure of #2 for the altitude from A to BC
5. Solve the two equations from #3 and #4
that point will be your orthocentre.
notice we did not use the altitude from B to AC
You could verify your answer is correct by finding that third altitude and solving it with one of the other two. You WILL get the same answer unless you made a mistake.