Question

In what ratio does the line x -y - 2 = 0 divides the line segment joining (3, -1) and (8, 9) ?

Answer 1

Let the line `y-x+2=0` divides the line segment joining the points (3, -1) and (8, 9) in the ratio `k:1`.
`therefore` Co-ordinates of `P-=((8k+3)/(k+1),(9k-1)/(k+1))`
but this point P lies on the line `" "y-x+2=0`

`therefore" "(9k-1)/(k+1)-(8k+3)/(k+1)+2=0`
`rArr" "9k-1-8k-3+2k+2=0`
`rArr" "3k=2 `
`rArr" "k=(2)/(3)`
`therefore` Required ratio =`(2)/(3) : 1=2:3`