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# 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. - Mathematics

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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.

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#### 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

Concept: Similarity of Triangles
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