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Question
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
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Solution
The points are P (a,-11),Q(5,b) , R (2,15) and S(1,1).
Join PR and QS, intersecting at O.
We know that the diagonals of a parallelogram bisect each other Therefore, O is the midpoint of PR as well as QS.
`"Midpoint of PR" = ((a+2)/2,(-11+15)/2) = ((a+2)/2,4/2) = ((a+2)/2,2)`
`"Midpoint of QS " = ((5+1)/2 , (b+1)/2) = (6/2 ,(b+1)/2) = (3,(b+1)/2)`
Therefore , `(a+2)/2 =3, (b+1)/2= 2`
⇒ a +2 = 6, b+1=4
⇒ a = 6 - 2, b = 4-1
⇒ a = 4 and b= 3
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