Question

The ratio in which the point `P(3/4, 5/12)` divides the line segment joining the points `A(1/2, 3/2)` and B(2, –5) is ______.

Answer 1

The ratio in which the point `P(3/4, 5/12)` divides the line segment joining the points `A(1/2, 3/2)` and B(2, –5) is 1 : 5.

Explanation:

Let AP : PB = k : 1.

By the section formula,

x-coordinate of `P = (k xx 2 + 1 xx (1/2))/(k + 1) = 3/4` 

And y-coordinate = `(k xx (-5) + 1 xx (3/2))/(k + 1) = 5/12`

Using the x-equation:

`(2k + 1/2)/(k + 1) = 3/4` 

⇒ 8k + 2 = 3k + 3

⇒ 5k = 1

⇒ k = `1/5` 

Checking with the y-equation gives the same k.

Hence AP : PB = 1 : 5.