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Question
Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
Solution
Let the given line divide the line segment joining the points A(2, −2) and B(3, 7) in a ratio k : 1
Coordinates of the point of division = ` ((3k+2)/(k+1), (7k-2)/(k+1))`
This point also lies on 2x + y − 4 = 0
`:.2((3k+2)/(k+1))+((7k-2)/(k+1))-1=0`
`=>(6k+4+7k-2-4k-4)/(k+1)=0`
`=>9k-2=0`
`=>k=2/9`
Therefore, the ratio in which the line 2x + y − 4 = 0 divides the line segment joining the points A(2, −2) and B(3, 7) is 2:9.
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