The coordinates of the centroid of a triangle whose vertices are (1, 1), (3, 3), and (2, 2) are ________.

We know, the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) = $\left(\frac{{\mathrm{x}}_1 + {\mathrm{x}}_2 + {\mathrm{x}}_3}{3} , \frac{{\mathrm{y}}_1 + {\mathrm{y}}_2 + {\mathrm{y}}_3}{3} \right)$

Given vertices of triangle:  (1, 1), (3, 3), and (2, 2)

Here, x₁ = 1, x₂ = 3, x₃ = 2, y₁ = 1, y₂ = 3 and y₃ = 2

On substitution, we get:

The coordinates of the centroid of the required triangle are = $(\frac{1+3+2}{3},\frac{1+3+2}{3})$

The coordinates of the centroid of the required triangle are = $(\frac{6}{3},\frac{6}{3})=(2,2)$