If A (-2,1),B (a,0),C (4,b),D (1,2) are the vertices of parallelogram ABCD ,find the value of a and b . Hence find the length of its sides.

diagonals of a parallelogram bisect each other
i.e the mid-points of AC and BD are equal.
(-2+4)/2, (1+b)/2 = (a+1)/2, (2+0)/2
(-2+4)/2 = (a+1)/2 ; (1+b)/2 = (2+0)/2
-2/2 =(a+1)/2 ; (1+b)/2 = 2/2
a+1=-2 ; 1+b=1
a=-3; b=0
length of AB² = (-2+3)² + (1-0)²
                      = 1+1
                      = 2  
               AB= root 2 cm
length BC²= (-3-4)² +(0-0)^{2
                      = 49+0
                      = 49
              BC= 7cm
AB=DC= root2cm BC=AD=7cm
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