Question

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

Answer 1

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

As we know that,

• Diagonals of Parallelogram bisects each other at a point.

Therefore,

Diagonals AC and BD bisecting each other at point O. Hence, O is the mid – point of AC and BD.

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▪︎ Mid – point formula is used to find out the mid – points on any line.

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$\qquad\quad\star\:{\underline{\boxed{\sf{ Mid - point = \bigg(\dfrac{x_{1} + x_{2}}{2} \bigg)}}}}$

¤ Mid – Point of AC :

$\dashrightarrow\sf \Bigg(\dfrac{6 + 9}{2}\Bigg) = \Bigg(\dfrac{15}{2}\Bigg) \qquad\qquad\bigg\lgroup\sf eq^n\;(1)\bigg\rgroup$

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¤ Mid – Point of BD :

$\dashrightarrow\sf \Bigg(\dfrac{8 + p}{2} \Bigg)\qquad\qquad\bigg\lgroup\sf eq^n\;(2)\bigg\rgroup$

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✇ Now Comparing eqⁿ ( 1 ) with eqⁿ ( 2 ) —

$\dashrightarrow\sf \dfrac{8 + p}{2} = \dfrac{15}{2}\\\\\\\dashrightarrow\sf 8 + p = 15\\\\\\\dashrightarrow\sf p = 15 - 8\\\\\\\dashrightarrow{\pmb{\sf{\red{p = 7}}}}$

$\therefore{\underline{\textsf{Hence, the required value of p is \textbf{7}}}.}$

Answer 2

Given :-

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

To Find :-

Value of p

Solution :-

Let the Point P be between the Parllelogram

Now

Diagonal will be AC and BD

Diagonal of parallelogram are always equal

AC = BD

Mid point = x₁ + x₂/2

(6 + 9/2) = (p + 8/2)

(15/2) = (p + 8/2)

2(15) = 2(p + 8)

30 = 2p + 16

30 - 16 = 2p

14 = 2p

14/2 = p

7 = p

Value of p is 7

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