Question

Find the area of the triangle whose vertices are mid points of the sides of the triangle whose vertices are A (2,1), B(4, 3) and C(2, 5).

Answer 1

let vertices of triangle be P,Q and R

By mid pt formula we can find co-ordinates of P,Q and R

-->P= ( 2+4/2 , 3+1/2)

     =(3,2) = (a,b)

-->Q= (2+2/2,5+1/2)

     = (2,3) = (c,d)

-->R = (4+2/2,5+3/2)

     = (3,4) = (e,f)

-->Area of trianglePQR = 1/2|[a(d-f) + c(f-b) + e(b-d)]|

                                      = 1/2|[3(3-4) + 2(4-2) + 3(2-3)]|

                                      =1/2|[-2]|

                                     = 1 unit ^ 2