Question

The ratio in which the line segment joining points A (a₁, b₁) and B (a₂, b₂) is divided by y-axis is

Options

• −a₁ : a₂

•  a₁ : a₂

• b₁ : b₂

•  −b₁ : b₂

Answer 1

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`