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The line segment joining the points P (3, 3) and Q (6, - 6) is bisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

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We are given PQ is the line segment, A and B are the points of trisection of PQ.

We know that PA:QA =1:2 So, the coordinates of A are

Since, A lies on the line

⇒ k= -8

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