Three vertices of a triangle are `A (1, 2), B (-3, 6) and C(5, 4)`. If D, E and F are the mid-points of the sides opposite to the vertices A, B and C, respectively, show that the area of triangle ABC is four times the area of triangle DEF.

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 .

If D and E are the mid-points of sides AB and AC of a triangle A B C respectively, show that vec B E+ vec D C=3/2 vec B Cdot

If D ,\ E and F are the mid-points of the sides of a /_\A B C , the ratio of the areas of the triangles D E F and ABC 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 the mid points of the side B C ,\ C A and A B respectively of a triangle ABC, write the value of vec A D+ vec B E+ vec C Fdot

If (-3, 2), (1, -2) and (5, 6) are the mid-points of the sides of a triangle, find the coordinates of the vertices of the triangle.

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .

If veca , vecb, vecc are the position vectors of the vertices. A,B,C of a triangle ABC. Then the area of triangle ABC is