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If the points A(6,1), B(8,2), C(9,4) and D(p,3) are the vertices of a parallelogram taken in order, find the value of p.

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If the points A(6,1), B(8,2), C(9,4) and D(p,3) are the vertices of a parallelogram taken in order, find the value of p.

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Let the points be A(6,1), B(8,2), C(9,4) and D(p,3)

We know that diagonals of parallelogram bisect each other.

∴ Midpoint of AC = Midpoint of BD …(i)

Coordinates of the midpoint of AC are

⇒ 8 + p = 15

⇒ p = 15 – 8 = 7

Hence, the value of p is 7

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