how do you find the orthocenter of a triangle algebraically?

Question

first how do you find the altitudes, then what do you do to find the orthocenter? without graphing it how do you do it algebraically? thanks to anyone who helps me! this big project is due tomorrow...and of course...i put it off...lol

thats the problem i cant plot it out on a graph, well i can to check my work, but i gotta do it with equations and stuff, thats how my teacher wants it in this stupid packet thing...ugh. evil.

Answer 1

The altitudes of a triangle are formed by running lines from the vertices and perpendicular to the opposite sides. The orthocenter is where they meet. Check out the wolfram site below. Now, if you mean by "finding the orthocenter", you mean to actually locate the coordinates of the orthocenter, I recommend you do it through coordinate geometry, develop equations for all the lines and altitudes of a triangle, and then find the coordinates of the intersection point of any pair of altitudes. There isn't hardly any space here to work it all out, but it's the most direct way to get at the answer. I hope you know how to do coordinate geometry.