In the given figure, G is the centroid of the triangle ABC. What are the coordinates of the vertex A?

Let (a, b) be the co-ordinates of the vertex A.

It is given that G is the centroid of ΔABC.

$\left(\frac{10}{3},-\frac{7}{3}\right)=\left(\frac{a+2+6}{3},\frac{b-4-4}{3}\right)$

$\Rightarrow \left(\frac{10}{3},-\frac{7}{3}\right)=\left(\frac{a+8}{3},\frac{b-8}{3}\right)$

$\Rightarrow 10=a+8, -7=b-8$

$\Rightarrow a=2, b=1$

Thus, the coordinates of the vertex A are (2, 1).