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Orthocentre of a triangle is the point of intersection of its 3 altitudes. A and B denote the 2 given vertices.
find out the slope of AB.
now, AB is perpendicular to the altitude from C.
name the co-ordinates of C as (a,b).
find out the slope of CO where O denotes the orthocentre.
this slope is perpendicular to the slope of AB.
next, take the side, say AC, find its slope. then, find the slope of BO. These 2 slopes are perpendicular to each other and hence, have the product -1.
now, you have got 2 equations to solve for 2 variables which are a,b for the third vertex.
if you still have doubts, ask :)
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