The coordinates of a triangle are A(6,0), B(0,6), C(6,6). Find the orthocenter using {q(y2-y1), -q(x2-x1)} where q= (x1x2+y1y1)/(x1y2-x2y1)``

Hello!

This triangle is a right one: the side BC is horizontal and the side AC is vertical, therefore the angle C is right.

For a right triangle, both legs are also its altitudes. Their intersection is the vertex of a right triangle, therefore it is the orthocenter.

So the answer is O(6,6). It is possible that the expressions involving q have some relation to the orthocenter, but for this case they are excess.