If $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$ are the vertices of a triangle,then where does the centroid of the triangle lie?

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

If a $\triangle ABC$ has vertices $A(-1, 7)$,$B(-7, 1)$ and $C(5, -5)$,then its orthocentre has coordinates

What is the circumcenter of the triangle with vertices $(0, 0)$,$(3, 0)$,and $(0, 4)$?

The orthocentre of a $\Delta ABC$ is $B$ and the circumcentre is $S(a, b)$. If $A$ is the origin,then the coordinates of $C$ are-

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.