Q7 of 157 Page 760

If A(1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a llgm ABCD then the value of x is

Since the given quadrilateral is a parallelogram, the length of parallel sides is equal.


So by distance formula,


⇒ Distance AB =


= √(4 + 1)


= √5


⇒ Distance CD =


=


⇒ Distance CD = Distance AB


⇒ =


Squaring both sides


⇒ 5 = (x-2)2 + 1


⇒ 4 = (x-2)2


Taking square root of both sides


⇒ 2 = x-2


⇒ x = 4


or


⇒ -2 = x-2


⇒ x = 0


Therefore the value of x can be 0 or 4.

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