Question

Find the ratio in which the line y = -1 divides the line segment joining (6, 5) and (-2, -11). Find the coordinates of the point of intersection. 

Answer 1

Let R (x, -1) be the point on the line y = - 1 which divides the line segment PQ in the ratio k: 1. 

Coordinates of R are, 

x = `(2"k" + 6)/("k" + 1) ,`      -1 = `(-11 "k" + 5)/("k" + 1)`

x = `(-2 (3/5) + 6)/(3/5 + 1),   => - "k" - 1 = - 11 "k" + 5`

`=>  "x"  = (-6 + 30)/8        => 10 "k" = 6`

x = 3        ⇒ k = 3/5   .....(1)

Hence, the required ratio is 3: 5 and the point of inter sec tion is (3, - 1).