Posted by **Anonymous** on Thursday, December 27, 2012 at 12:56pm.

Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0

- maths -
**Reiny**, Thursday, December 27, 2012 at 2:19pm
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.

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