1. The problem statement, all variables and given/known data There are three problems based on the following diagram. You have a triangle on the cartesian plane with each corner having the coordinates (-a, 0) (a,0) (b,c) Find the coordinates (in terms of a,b,c) of the point where all three perpendicular bisectors of the triangle intersect. Find the coordinates (in terms of a,b,c) of the point where all three medians of the triangle intersect. Find the coordinates (in terms of a,b,c) of the point where all three altitudes of the triangle intersect. Prove that all three points lie on one line. 2. Relevant equations Well as far as I know you can't use any calculus on this problem (as it came in the section before calculus started) although I don't believe you should have to. 3. The attempt at a solution I basically was trying to use the slopes, distance formula, pythagorean theorem, and law of sines to play around with this one but I'm still pretty clueless. I believe the line that they lie on is the euler line although I know nothing about that or any of the other central points of a triangle.