# in triangle ABC the coordinates of vertex A are (0,-1) D(1,0) and E(0,1) respectively the mid points of sides AB and AC . if F is the mid point of side BC , find the area of triangle DEF.

Dear Student,

We form our diagram from given information , As : We know formula for coordinate of mid point ( x , y ) =

As D is mid point of AB , So x  =  1 , y  = 0  and x1 = 0, x2x and  y1 = - 1 , y2y  , ( As we assume coordinate of B(x,y ) ), So

So, Coordinate of B ( 2 , 1 )

Similarly , as E is mid point of AC , So x  =  0 , y  = 1  and x1 = 0, x2m and  y1 = - 1 , y2m  , ( As we assume coordinate of C (m,n ) ), So

So, Coordinate of C ( 0 , 3 )

We assume coordinate of F ( p,q ), So x1 = 2, x2 =  0 and  y1 = 1 , y2 = 3  , As F is mid point of BC

We know area of triangle from given three points  :

Area  =

To find area of triangle ABC , Here x1 = 0 , x2 =  2 , x3 = 0  and  y1 = - 1 , y2 =  1 , y3 = 3

So,

Area of triangle ABC  = = 4 unit square

And

To find area of triangle DEF , Here x1 = 1 , x2 =  0 , x3 = 1  and  y1 = 0 , y2 =  1 , y3 = 2

So,

Area of triangle DEF  = = 1 unit square