A triangle ABC is placed so that the mid-points of the sides are on the x,y,z axes. Lengths of the intercepts made by
the plane containing the triangle on these axes are respectively α,β,γ .Coordinates of the centroid of the triangle ABC are
(−α/3,β/3,γ/3)
(α/3,−β/3,γ/3)
(α/3,β/3,−γ/3)
(α/3,β/3,γ/3)
Let D,E,F be the midpoints of the sides BC, CA and AB respectively.
Then D=α,0,0, E=0,β,0 and F=0,0,γ
We know that centroid of the triangle is same as centroid of the triangle formed with midpoints D,E,F.
⇒Centroid=G=α3,β3,γ3