You are given with a triangle ABC having orthocentre H. You know the coordinates of 2 vertices A and B and the ortho centre H. How would you proceed to find the third vertex ?
What I've done : I assumed a triangle ABH and found the orthocentre for that triangle. The orthocentre comes out to be C. Is this a proper method or was I just lucky to get the answer ?
Also if the method is correct, is there any shorter method to find the same either by formula or geometrically.
This is correct; the orthocentre of $ABH$ is always $C$. Indeed, we have $AC \perp BH$ (since $BH$ is an altitude) and $BC \perp AH$ (since $AH$ is an altitude). So the perpendiculars from $A$ to $BH$ and $B$ to $AH$ meet at $C$, and $C$ is the orthocentre of $ABH$.