find the ratio in which 3x+y-9=0 line divides the line segment joining A(1,3) and B(2,7)
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Suppose the line 3x + y – 9 = 0 divides the line joining A(1, 3) and B(2, 7) in the ratio of λ : 1 at point C.
Coordinate of C = (2λ + 1/λ + 1, 7λ + 3/λ + 1)
But point C lies on the line 3x + y – 9 = 0
Therefore,
3(2λ + 1/λ + 1) + (7λ + 3/λ + 1) – 9 = 0
⇒ 6λ + 3 + 7λ + 3 - 9λ – 9 = 0
⇒ 4λ – 3 = 0
⇒ λ = ¾
The required ratio = λ : 1
= 3 : 4
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