Q32 of 184 Page 10

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.


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



Coordinates of the midpoint of BD are



So, according to eq. (i), we have




⇒ 8 + p = 15


⇒ p = 15 – 8 = 7


Hence, the value of p is 7


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