If A (-2,1), B (a,0),C (4,b)and D(1,2)are the vertices of a parellogram Abcd find the value of a and b hence find the length of its sides?

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If A (-2,1), B (a,0),C (4,b)and D(1,2)are the vertices of a parellogram Abcd find the value of a and b hence find the length of its sides?

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If A (-2,1), B (a,0),C (4,b)and D(1,2)are the vertices of a parellogra...

In a parallelogram the diagonals bisect each other

Midpoint of AC = midpoint of BD

Midpoint formulae (x1+x2)/2 ; (y1+y2)/2

(-2+4)/2 ; (1+b)/2 = (a+1)/2 ; (0+2)/2

2/2 ; (1+b)/2 = (a+1)/2 ; 2/2

=> 1=(a+1)/2

a+1 = 2

a=1

=> (1+b)/2 = 1

1+b=2

b= 1

a=1 and b=1

Using distance formula we came find out the length of the sides of parallelogram

Distance formula √[(x2-x1)^2+(y2-y1)^2]

AB = √[(1+2)^2+(0-1)^2]

= √(9+1)

=√10u

BC = √[(4-1)^2+(1-0)^2]

= √(3^2+1^2)

= √10u

It is a rhombus as all the sides are equal.

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