If a vertex of a triangle is $\left(1,1\right)$ and the midpoint of two sides through this vertex are $\left(-1,2\right),\left(3,2\right)$ then the centroid of the triangle is

Given, vertex of a triangle is $\left(1,1\right)$

Midpoints of the sides passing through this vertex are $\left(-1,2\right),\left(3,2\right)$

Centroid divides median in $2:1$  ratio

$C=\left(\frac{2+1}{3},\frac{6+1}{3}\right)=\left(1,\frac{7}{3}\right)$