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Question
Find the ratio in which the line 2x + y = 4 divides the line segment joining the point P(2, –2) and Q(3, 7).
Solution
Let the line 2x + y = 4 divides the line segment joining the points P(2, –2) and Q(3, 7) in the ratio k : 1.
Then, we have
`(x, y) = ((3k + 2)/(k + 1),(7k - 2)/(k + 1))`
Since `((3k + 2)/(k + 1),(7k - 2)/(k + 1))` lines on line 2x + y = 4, we have
`2(3k + 2/k + 1) + (7k - 2)/(k + 1) = 4`
`=>` 6k + 4 + 7k – 2 = 4k + 4
`=>` 13k + 2 = 4k + 4
`=>` 9k = 2
`=> k = 2/9`
Hence, required ratio is 2 : 9
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