If A(2, 3), B((4, 6), C(7, 4) and D(a, b) are the vertices of a quadrilateral, such that diagonals AC and BD intersects each other O. If O is mid point of AC and BD then value of a and b are
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Let the three vertices of parallelogram ABCD be A(−1,2),B(4,1)andC(7,6)
Let the fourth vertex be D(a,b)
By joining AC and BD intersect at point O i.e, diagonals of parallelogram bisect each other
Mid point of AC= (
2
−1+7
,
2
2+6
)=(3,4)
Mid point of BD =(
2
4+a
,
2
1+b
)
2
4+a
=3
2
1+b
=4
∴a=2,b=7
∴ The coordinate of fourth vertex =(2,7)
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