Question

The line segment joining the points A( 2,1 ) and B ( 5 , - 8 ) is trisected at the points P and Q . Such that P is nearer to A .If P also lies on the line given by 2x -y + k = 0 . Find the value of K.

Answer 1

Answer The given point are A(2, 1) and B(5, – 8).

Given, P and Q trisects the line segment AB.

∴ AP = PQ = QB

PB = PQ + QB = AP + AP = 2AP

AP : PB = AP : 2AP = 1 : 2

∴ P divides the line segment AB in the ration 1 : 2.

∴ Coordinates of P

P(3, – 2) lies on 2x – y + k = 0.

∴ 2 × 3 – (– 2) + k = 0

⇒ 6 + 2 + k = 0

⇒ 8 + k = 0

⇒ k = – 8

Thus, the value of k is – 8.

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Answer 2

Step-by-step explanation:

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