Question

In what ratio does the line x – y – 2 = 0 divide the line segment joining the points A(3, –1) and B(8, 9)? 

Answer 1

Let the line x - y - 2 = 0  divide the line segment joining the points A (3, -1) and B (8, 9)  in the ratio k : 1 at P.

Then, the coordinates of P are

`"p" ((8"k"+3)/("k"+1),(9"k"-1)/("k"+1))`

Since, P lies on the line  x - y - 2 = 0 we have:

` ((8"k"+3)/("k"+1)) - ((9"k"-1)/("k"+1)) -2=0`

⇒ 8k + 3 - 9k + 1 - 2k - 2 = 0 

⇒ 8k - 9k - 2k + 3 + 1 - 2 = 0

⇒ - 3k + 2 = 0

⇒ - 3k = - 2

`⇒ "k" = 2/3`

So, the required ratio is  `2/3:1` which is equal to 2 : 3.