Question

Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).

Answer 1

Suppose the line 3x + y - 9 = 0 divides the line joining A(1, 3) and B(2, 7) in the ratio of λ: 1 at point C.

Coordinates of C = `((2λ + 1)/(λ + 1) , (7λ + 3)/(λ + 1))`
But point C lies on the line 3x + y - 9 = 0.
Therefore,
`3((2λ + 1)/(λ + 1)) + ((7λ + 3)/(λ + 1)) - 9` = 0
⇒ 6λ + 3 + 7λ + 3 - 9λ - 9 = 0
⇒ 4λ - 3 = 0
⇒ λ = `(3)/(4)`
The required ratio
= λ : 1
= 3 : 4.