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Question
Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.
Solution
The given points of the parallelogram are A(3, 1), B(5, 1), C(a, b) and D(4, 3).
We know that the diagonals of a parallelogram bisect each other. So, O is the midpoint of AC and DB.
So,
`((3+"a")/2 ,(1+"b")/2) =((5+4)/2, (1+3)/2)`
⇒ `((3+"a")/2 ,(1+"b")/2) = (9/2,4/2)`
⇒ `((3+"a")/2 ,(1+"b")/2) = (9/2,2)`
On comparing we get
`(3+"a")/2 =9/2`
⇒ 3 + a = 9
⇒ a = 6
Also,
`(1+"b")/2 = 2`
⇒ 1 +b = 4
⇒ b = 3
Thus , a = 6, b = 3
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