Math, asked by reetmalik23aug, 1 year ago

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

Answers

Answered by Aathan
326
a is equal to 1 and b is also equal to 1.
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Answered by mysticd
114

Solution :


Given A(-2,1), B(a,0),C(4,b),


and D(1,2) are vertices of a


Parallelogram ABCD.


We know that the diagonals


of a parallelogram bisects each


other .


So the midpoint of the diagonals


AC and DB should be same.


Now , we find the midpoint of


AC and DB by using


[ (x1+x2)/2 , (y1+y2)/2 ] formula.


Midpoint of AC=[(-2+4)/2,(1+b)/2]


= [ 1 , (1+b)/2 ] ----( 1 )


Midpoint of BD =[(a+1)/2,(0+2)/2]


= [ (a+1)/2 , 1 ] ---( 2 )


Midpoint of AC= midpoint of BD




i ) ( a + 1 )/2 = 1


=> a + 1 = 2


=> a = 1


ii ) ( 1 + b )/2 = 1


=> 1 + b = 2


=> b = 1


Therefore ,


a = 1 , b = 1


iii ) length of the side AB


A(-2,1) = ( x1, y1)


B(1,0) = ( x2, y2 )


AB = √(x2-x1)² + (y2-y1)²


= √(1+2)²+(0-1)²


= √3²+1²


= √10


iv ) Length of the side BC


BC = √(4-1)²+(1-0)²


= √3²+1²


= √10


Therefore ,


AB = CD = √10


BC = AD = √10


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