Question

Determine the ratio in which the line `3x+y-9=0` divides the segment joining the points (1,3) and `(2,7)dot`

Answer 1

Suppose the line `3x+y-9=0` divides the line segment joining `A(1,3)` and `B(2,7)` in the ratio `k:1` at point C. Then, the coordinates of C are
`((2k+1)/(k+1),(7k+3)/(k+1))`
But C lies on `3x+y-9=0`. Therefore,
`3((2k+1)/(k+1))+(7k+1)/(k+1)-9=0`
or `6k+3+7k+3-9k-9=0`
or `k=(3/4)`
So, the required ratio is `3:4` internally.