1. The problem statement, all variables and given/known data A triangle ABC is given where vertex A is (1,1) and the orthocentre is (2,4). Also sides AB and BC are members of the family of lines ax+by+c=0 where a,b,c are in Arithmetic Progression. Find vertex B. 2. Relevant equations 3. The attempt at a solution I can write the equation of AO (O being orthocentre). But I need to somehow get vertex B and I think I need to have some more equations to do that. Can someone explain me how to apply the second hint given in the question?