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?

If in triangle $ABC$,$A \equiv (1, 10)$,circumcentre $\equiv \left( -\frac{1}{3}, \frac{2}{3} \right)$ and orthocentre $\equiv \left( \frac{11}{3}, \frac{4}{3} \right)$,then the coordinates of the mid-point of the side opposite to $A$ are:

If $O, G, S$ are respectively the orthocentre,centroid and circumcentre of a triangle whose vertices are $A(2,3), B(2,4)$ and $C(4,3)$,then $AO^2 + 9BG^2 + 4CS^2 =$

If $A(2, 2)$,$B(-4, -4)$,and $C(5, -8)$ are the vertices of a triangle,then the length of the median passing through vertex $C$ is:

Let $A(1,1), B(1,-1), C(-1,1)$ be the vertices of $\triangle ABC$. Let $S$ be the circumcentre,$O$ be the orthocentre,and $I$ be the incentre of the $\triangle ABC$. Then $IS + OS =$ ?

If the vertices of a triangle are $A(1, 4)$,$B(3, 0)$,and $C(2, 1)$,then the length of the median passing through $C$ is