Question 870004
the middle points of the sides of a triangle are ( 2,1)(-1,-3) and ( 4,5) respectively . find the coordinates of the vertices of the triangle 
let vertex are A B  C  (x1,y1)(x2,y2)(x3,y3) respectively
using mid point formula  mid pint of AB is (2,1)
2= X1+X2/2   than X1 +X2 =4 (1)     and  Y1 +Y2 = 2 (4)
similarly for BC AND AC
             than X2 +X3 =-2 (2)   and  Y2 +Y3 = -6    (5)
                  X3 +X1 =  8 (3)  and  Y3 +Y1 = 10   (6)
by adding  equation  1 2 and 3 for  x  and adding  4   5  6 for y
2X1+2X2 +2X3 = 10     and 2Y1 +2Y2 +2Y3 = 6
by taking 2 common for both equations 

X1+X2 +X3 = 5 (7)    and  Y1 +Y2 +Y3 = 3  (8)
subtracting 1   2   3  from equation 7     and  4  5  6   from 8
X3=1  X1 = 3  X2 =-3     similarly     Y3 = 1 Y1 =9   Y2 = -7

Answer  vertex A =(3,9)    B =(-3,-7)   C =(1,1)