Question

The ratio in which the line segment joining P (x₁, y₁) and Q (x₂, y₂) is divided by x-axis is

Options

•  y₁ : y₂

• −y₁ : y₂

•  x₁ : x₂

•  −x₁ : x₂

Answer 1

Let C( x , 0)  be the point of intersection of x-axis with the line segment joining p(x_{1 ,}  y₁)  and  Q(x₂,y₂) which divides the line segment PQ 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,

`(x , 0) = ((λx_2 + x_1)/(λ+1) , (λy_2 + y_1)/(λ + 1))`

Now equate the y component on both the sides,

`(λy_2 + y_1)/(λ + 1) = 0`

On further simplification,

`λ = ( y_1) /(y_2)`