Question

In ∆ABC, AD median of BC where position vectors of A and D are 3i-2j and -3i-4j respectively. Find the position vector of centroid G of the ∆ABC.

Answer 1

The centroid is located 2/3 of the length of a median, measured from the vertex

OA = (3, -2)
OD = (-3, -4)
we know AG : GD = 2 : 1
OG =(1/3)(3,-2) + (2/3)(-3,-4)
= (1, -2/3) + (-2, -8,3)
= (-1, -10/3)

or -i - (10/3)j