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.

Answer 1

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`