Question

Find the co-ordinates of the centroid of the triangle whose vertices are (x₁, y₁, z₁) (x₂, y_2, z₂) and (x₃, y₃, z₃)

Answer 1

Note: Centroid is the point of intersection of the medians of the triangle and it is denoted by G. Centroid divides the median in the ratio 2:1.

Let A = (x₁, y₁, z₁) , B = (x₂, y₂, z₂) and C = (x₃, y₃, z₃) be the vertices of the triangle ABC. Let AD be the median drawn from A. Then D is the mid-point of BC.

Let G be the centroid of the ΔABC. median AD in the ratio 2 : 1. 

∴ The coordinates of G are,