Question

is there an equation to find the orthocenter of a triangle?

Answer 1

equilateral triangle?

Answer 2

umm, any triangle i guess

Answer 3

does it matter?

Answer 4

Suppose you are given the three vertices A,B and C, and the equations of the sides BC, CA and AB are La,Lb and Lc.
The orthocentre would be a line passing through a vertex and perpendicular to the opposite side, such as : through A and perpendicular to La.

I think formulas would be more complicated than working with the basic geometrical concepts (perpendicularity, through a point, etc.)

Answer 5

thanks!

Answer 6

You're welcome!

Answer 7

If you make the origin the center of the circumcircle (the circle the triangle fits in), then the orthocenter is A+B+C, treating them as vectors.

Answer 8

so if you find the slope of each of the segments, just find the opp reciprical and draw a line?

Answer 9

Graphically, just drop a perpendicular from each vertex to the leg (or its extension) opposite the angle. All three altitudes meet at the orthocenter

Answer 10

perfect, thanks again!