Question

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

Answer 1

Hi, frnd. Hope this solution helps you..

Answer 2

Answer:

$p = 7 , \: q = 4$

Step-by-step explanation:

$Given \: A(6,1), B(8,2), C(9,q) \:and \: D(p,3)\\are\: the\: vertices\:of\:a\: parallelogram$

$Midpoint\:of\:BD = Midpoint\:of\:AC$

$\pink {( Diagonals \:bisects \: eachother )}$

$\left(\frac{8+p}{2},\frac{2+3}{2}\right) =\left(\frac{6+9}{2},\frac{1+q}{2}\right)$

$\implies \left(\frac{8+p}{2},\frac{5}{2}\right) =\left(\frac{15}{2},\frac{1+q}{2}\right)$

$\implies \frac{8+p}{2} = \frac{15}{2},\:and\:\frac{5}{2} = \frac{1+q}{2}$

$\implies 8+p = 15 ,\: and \: 5 = 1+q$

$\implies p = 15 - 8 , \: and \: q = 5 - 1$

$\implies p = 7 , \:and \: q = 4$

Therefore.,

$p = 7 , \: q = 4$

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