Question

If D, E, F are the mid-points of the sides of a triangle ABC, prove by vector method that area of ∆DEF = 1/4  (area of ∆ABC).

Answer 1

Taking A as the origin, let the position vectors of B and C be vector b and c  respectively. Then, the position vectors of D, E and F are  

= 1/4 (vector area of ∆ABC)

Hence, area of ∆DEF = 1/4  area of ∆ABC.