If two vertices of a triangle are $(5, -1)$ and $(-2, 3)$ and its orthocenter is at $(0, 0)$,find the third vertex.

The orthocenter of the triangle whose sides are given by $x+y+10=0$,$x-y-2=0$,and $2x+y-7=0$ is

If $A(4, -3)$,$B(3, -2)$,and $C(2, 8)$ are the vertices of a triangle,what is the distance of its centroid from the $y$-axis?

The centroid of the triangle $ABC$,where $A \equiv (2,3)$,$B \equiv (8,10)$,and $C \equiv (5,5)$ is

Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.
Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.

If the coordinates of the orthocenter and the centroid of a triangle are $(4, -1)$ and $(2, 1)$ respectively,then what are the coordinates of the circumcenter of the triangle?