If two vertices of a triangle are (-2, 3) and (5, -l), the orthocenter lies at the origin, and the centroid on the line  x+y=7, then the third vertex lies at

Suppose that the third vertex is A(h,k)  BC is perpendicular to AO because O is orthocenter   Hence, kh×-47=-1 4h-7k=0  The centroid of the triangle lies on x+y=7  -2+5+h3,3-1+k3 lies on x+y=7 3+h+2+k=21 h+k=16 solving the above two equations  7k+4k=64 11k=64 k=6411, h=11211  Third vertex is 6411,11211