Question

Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection. 

Answer 1

Let P (-2, y) be the pcint on line x which divides the line segment AB the ratio k : 1.

Coordinates of P are 

`- 2 = ("k" - 6)/("k" + 1) ,`

⇒  -2k - 2 = k - 6  

⇒  -3k = - 4 

⇒  k = `4/3`  .....(1)

`=> "k " = 4/3 `

y = `(6"k" - 1)/("k + 1")`

`=> "y" = (69 (4/3) - 1)/(4/3 + 1)`   ...from (1)

`=> "y" = (24 - 3)/7 `

⇒  y = 3

Hence, the required ratio is 4: 3 and the point of intersection is (-2, 3).