Two vertices of a triangle are $(0, 2)$ and $(4, 3)$. If its orthocenter is at the origin $(0, 0)$,then its third vertex lies in which quadrant?

The orthocentre of the triangle with vertices $(-2, -6)$,$(-2, 4)$ and $(1, 3)$ is

Let $A(1,0), B(6,2)$ and $C(\frac{3}{2}, 6)$ be the vertices of a triangle $ABC$. If $P$ is a point inside the triangle $ABC$ such that the triangles $APC, APB$ and $BPC$ have equal areas,then the length of the line segment $PQ,$ where $Q$ is the point $(-\frac{7}{6}, -\frac{1}{3})$ is

The centroid of the triangle formed by the lines $x-3y+3=0$,$x+3y+3=0$,and $x+y-1=0$ is

The orthocentre of the triangle whose vertices are $(0, 0)$,$(3, 0)$,and $(0, 4)$ is

If two vertices of a triangle are $(6, 4)$ and $(2, 6)$ and its centroid is $(4, 6)$,then the third vertex is