Find the coordinates of the centroid of a triangle whose vertices are :

A(-1, 3), B(1, -1) and C(5, 1).

Coordinates of the centroid of the triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by

$\Big(\dfrac{x$1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big)

Putting values in the formula we get,

$= \Big(\dfrac{-1 + 1 + 5}{3}, \dfrac{3 + (-1) + 1}{3}\Big) \\[1em] = \Big(\dfrac{5}{3}, \dfrac{3}{3}\Big) \\[1em] = \Big(\dfrac{5}{3}, 1\Big).$

Hence, the coordinates of the centroid of the triangle are $\Big(\dfrac{5}{3}, 1\Big)$.