Question

In what ratio does the point (1, a) divided the join of (−1, 4) and (4, −1) Also, find the value of a. 

Answer 1

Let the point P (1, a) divides the line segment AB in the ratio k : 1.

Coordinates of P are,

`1 = (4"k" - 1)/("k" + 1) ,`

⇒ k + 1 = 4k − 1

⇒ 2 = 3k

⇒ k = `2/3`      ...(1)

⇒ a = `(-"k" + 4)/("k" + 1)`

⇒ a = `(-2/3 + 4)/(2/3 + 1)`    ...(from (1))

⇒ a = `10/5 = 2`

Hence, the required ratio is 2 : 3 and the value of a is 2.