Question

Find the ratio in which the point P (2, 4) divides the line joining points (-3, 1) and (7, 6). 

Answer 1

Let the point P divides AB in the ratio k : 1.

Coordinates of P are 

x = `(7"k" - 3)/("k" + 1)`

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

But given, P(x, y) =P(2, 4) 

`therefore 2 = (7"k" - 3)/("k" + 1)`

⇒ 2k + 2 = 7k - 3 

⇒ 5 = 5k

⇒ k = 1

k : 1 = 1 : 1

or `4 = (6"k" + 1)/("k" + 1)`

4k + 4 = 6k + 1

⇒ 3 = 2k

⇒ k = `3/2`

k : 1=3 : 2