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Question
The line 5x + 3y = 25 divides the join of (b,4) and (5, 8) in the ratio of 1 : 3. Find the value of b.
Solution
Let the point of intersection of PQ and the line 5x+3y=25, be the point R(x,y)
Also, given the line 5x + 3y = 25 divides the line segment PQ in the ratio 1 :3.
i.e. PR : RQ = 1 : 3
Coordinates of Rare,
R (x,y) = R `((5 + 3"b")/4 , (8 + 12)/4) = "R" ((5 + 3"b" )/4 , 5)`
R (x,y) lies on the line 5x + 3y = 25
R will satisfy the equation of the line
5`((5 + 3"b")/4)` + 3 (5) = 25
⇒ 5`((5 + 3"b")/4)` = 10
⇒ 5 + 3b = 8
⇒ 3b = 3
⇒ b = 1
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