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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.
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Solution
As a line segment, AB is trisected by the points P and Q, Therefore.
Case l: When AP: PB = 1: 2.
Then, coordinates of P are
`{{1xx5 +2xx2)/(1+2) , (1xx(-8)+1xx2)/(1+2)}`
Implies that
P(3, -2)
Since the point P{3, - 2) lies on the line
2x - y + k = 0
⇒ 2 × 3 -(-2) + k = 0
⇒ k = -8
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