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Question
The line 5x - 3y +1 = 0 divides the join of (2,m) and (7,9) in the ratio 2: 3. Find the value of m.
Solution
Let the point of intersection of PQ and 5x - 3y + 1 = 0 be the point R( a, b ).
Also given the line 5x -3y+ 1=0 divides the line segment PQ in the ratio 2:3,
i.e. PR : PQ = 2 : 5
Coordinates of R are,
R (a,b) = R `((14 + 6)/5 , (18 + 3"m")/5) = "R" (4, (18 + 3"m")/5)`
R (a,b) lies on the line 5x - 3y + 1 = 0
R will satisfy the equation of the line
5(4) - 3 `((18 = 3"m")/5)` + 1 = 0
⇒ -3 `((18 + 3"m")/5)` = -21
⇒ 18 + 3m = 35
⇒ 3m = 17
⇒ m = `17/3`
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