Two vertices of a triangle are . If the orthocenter of the triangle is the origin,find the third vertex.
Let be the given vertices and be the third vertex.
Let AD and BE be the altitudes meeting at the orthocenter O(0,0) of the triangle.
AD is perpendicular to BC,therefore let this be equation 1.
Similar to the above,.Let this be equation 2.
Solving the two equations,we get
Therefore the third vertex is