Question

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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.

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Answer 1

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Answer 2

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WE KNOW THAT DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER. 

So,

THE COORDINATES OF THE MID-POINT OF AC = COORDINATES OF THE MID-POINT OF BD 

 

$COORDINATE \: \: \: OF \: \: X\\ \\ \frac{(6 + 9)}{2} = \frac{8 + p}{2} \\ = > 15 = 8 + p \\ = > p = 15 - 8 \\ = > p = 7$
$COORDINATE \: \: OF \: \: Y \\ \\ = > \frac{1 + p}{2} = \frac{2 + 3}{2} \\ = >p + 1 = 5 \\ = > p = 5 - 1 \\ = > p = 4$