Let points D,E,F be the midle points of sides BC,CA and AB respectively of `/_\ABC` and P is the middle points of CD. Lines FD and P meet the median BE and Q and R respectively. Proving using vector method that((area of quadrilaterial DPRQ)/(area of `/_\ABC`))=11/56.

Let the area of a given triangle ABC be Delta . Points A_1, B_1, and C_1 , are the mid points of the sides BC,CA and AB respectively. Point A_2 is the mid point of CA_1 . Lines C_1A_1 and A A_2 meet the median BB_1 points E and D respectively. If Delta_1 be the area of the quadrilateral A_1A_2DE , using vectors or otherwise find the value of Delta_1/Delta

If D, E and F be the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC and G is the centroid of the triangle, then vec(GD) + vec(GE) + vec(GF) =

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.

D, E and F are the mid-points of the sides AB, BC and CA respectively of A ABC. AE meets DF at O. P and Q are the mid-points of OB and OC respectively. Prove that DPOF is a parallelogram.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

If D(3,-2) , E(-3,1) and F(4,-3) are the mid-points of the sides BC, CA and AB respectively of Delta ABC , find the co-ordinates of point A , B and C .

If D ,Ea n dF are the mid-points of sides BC, CA and AB respectively of a A B C , then using coordinate geometry prove that Area of △DEF= 1/4 (Area of △ABC)

In Delta ABC, D,E and F are mid-point of sides AB ,BC and AC respectively , Prove that AE and DF bisect each other.

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF