Question

Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the line x - y + 2 = 0, then value of k is ______.

Options

• `2/3`

• `1/2`

• `1/3`

• `1/4`

Answer 1

Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the line x - y + 2 = 0, then value of k is `underline(2/3)`.

Explanation:-

Since P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1

∴ coordinates of P are `((9k-1)/(k+1), (8k+3)/(k+1))`

Since P lies on the line x - y + 2 = 0, then `(9k-1)/(k+1)-(8k+3)/(k+1)+2=0`

9k -1 - 8k - 3 + 2k + 2 = 0

which gives

`"k"=2/3`