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.

Answer 1

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