The ratio in which the line segment joining points *A* (*a*_{1}, *b*_{1}) and *B* (*a*_{2}, *b*_{2}) is divided by *y*-axis is

#### Options

−

*a*_{1}:*a*_{2}*a*_{1}_{ }:*a*_{2}*b*_{1}:*b*_{2}−

*b*_{1}:*b*_{2}

#### Solution

Let P( 0 ,y) be the point of intersection of *y-*axis with the line segment joining` A(a_1 , b_1) " and B " (a_2 , b_2)` which divides the line segment AB in the ratio λ : 1 .

Now according to the section formula if point a point P divides a line segment joining `A(x_1 ,y_1) " and" B (x_2 , y_2)` in the ratio *m:n* internally than,

`P ( x, y) = ((nx_1 + mx_2)/(m+n) , (ny_1 +my_2)/(m + n))`

Now we will use section formula as,

`( 0, y) = ((λa_2 +a_1)/(λ + 1) , ( λb_2 + b_1) /(λ + 1))`

Now equate the *x* component on both the sides,

`(λa_2 + a_1) /(λ + 1) = 0`

On further simplification,

`λ = - a_1/a_2`