If A, B, C are the points `(-1, 5), (3, 1), (5, 7)` respectively and D, E, F are the middle points of BC, CA and AB respectively, prove that Area of `DeltaABC=4 DeltaDEF`.

Thevertices of a triangle ABC are A(-7, 8), B (5, 2) and C(11,0) . If D, E, F are the mid-points of the sides BC, CA and AB respectively, show that DeltaABC=4 DeltaDEF .

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.

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .

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.

In a trapezium ABCD, if E and F be the mid-points of diagonal AC and BD respectively. Prove that EF=1/2(AB-CD).

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 triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.

If D, E, F are respectively the mid-points of AB, AC and BC respectively in a Delta ABC, " then " vec (BE) + vec(AF) =

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 .

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.