Question

Find the ratio in which the line segment joining the points A (3, 8) and B (–9, 3) is divided by the Y– axis.

Answer 1

Let C be a point on Y-axis which divides seg AB in the ratio m:n.

We are given two points:

• A (3, 8)

• B (−9, 3)

A point lies on the Y-axis if its x-coordinate is 0.

Let the Y-axis divide the line segment AB in the ratio: m:n

`((nx_1 + mx_2)/(m+n), (ny_1 + my_2)/(m+n))`

• A(x₁, y₁) = (3, 8)

• B(x₂, y₂) = (−9, 3).

`(n(3) + m(-9))/(m+n) = 0`

3n − 9m = 0

`=> 3n = 9m => n/m = 9/3 = 3`

`=> m/n = 1/3`

= 1:3