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# If A(–2, 1), B(A, 0), C(4, B) and D(1, 2) Are the Vertices of a Parallelogram Abcd, Find the Values of a and B. Hence Find the Lengths of Its Sides - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides

#### Solution

We know that diagonals of a parallelogram bisect each other.

Coordinates of the midpoint of AC = coordinates of the midpoint of BD

the midpoint of AC = midpoint of BD

=> ((4-2)/2, (b+1)/2) = ((a+1)/2 , (0 +2)/2)

=> (2/2, (b+1)/2)  = ((a+1)/2 , 2/2)

=> (1, (b+1)/2) = ((a+1)/2 , 1)

So

1 = (a+1)/2

2 = a + 1

:. a = 1

and

(b +1)/2 = 1

=> b + 1 = 2

:. b = 1

Therefore, the coordinates are A(–2, 1), B(1, 0), C(4, 1) and D(1, 2).

AB = DC = sqrt((1+2)^2 + (0 - 1)^2) = sqrt(9 + 1) = sqrt(10)

AD = BC = sqrt((1+2)^2 + (2-1)^2) = sqrt(9 + 1) = sqrt10`

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Solution If A(–2, 1), B(A, 0), C(4, B) and D(1, 2) Are the Vertices of a Parallelogram Abcd, Find the Values of a and B. Hence Find the Lengths of Its Sides Concept: Concepts of Coordinate Geometry.
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