The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12), and (8, 0) 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:  (0, 6), (8,12), and (8, 0)

Here, x₁ = 0, x₂ = 8, x₃ = 8, y₁ = 6, y₂ = 12 and y₃ = 0

On substitution, we get:

The coordinates of the centroid of the required triangle are = $(\frac{0+8+8}{3},\frac{6+12+0}{3})$

The coordinates of the centroid of the required triangle are = $(\frac{16}{3},\frac{18}{3})=(\frac{16}{3},6)$