Question

Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex. 

Answer 1

Given the centroid of Δ ABC is at origin , i.e. G (0 , 0).

Let the coordinates of third vertex be (x , y).

Coordinates of G are ,

G (0 , 0) = G `((1 + 3 + "x")/3 , (4 + 1 + "y")/3)`

O = `(4 + "x")/2` , O = `(5 + "y")/2`

x = - 4 , y = -5

Coordinates of third vertex are (-4 , -5)