Median of a Triangle and its Properties

If the coordinates of the three verticals of a triangle are $(3, -5), (-6, 4) and (9, -8)$ find the coordinates of the centroid of the triangle.

If the coordinates of the three verticals of a triangle are $(-2, 5), (-4, -3) and (6, -2)$ find the coordinates of the centroid of the triangle.

The point of concurrency of the medians of a triangle is known as _____

Vertices of a $∆ABC$ are $A\left(1, 2\right), B\left(5, 7\right) \& C\left(11, 13\right)$, then the length of the median through $C$ is $\sqrt{k}$, then find the value of $k$.

Vertices of a $∆ABC$ are $A\left(2, 2\right), B\left(-4, -4\right) \& C\left(5, -8\right)$, then the length of the median through $C$ is $\sqrt{k}$, then find the value of $k$.

In the given figure, $G$ is the point of concurrence of medians of $∆ABC$. If $GF=5 \mathrm{cm}$, find the length of $AF$

The length of hypotenuse of a right-angled triangle is $18 \mathrm{cm}$. Find the length of median of its hypotenuse.