Question

Write the ratio in which the line segment joining points (2, 3) and (3, –2) is divided by x-axis.

Answer 1

Let P (x, 0) be the point of intersection of x-axis with the line segment joining A (2, 3) and B (3, −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,

`(x, 0) = ((3λ +2)/(λ + 1), (3 - 2λ)/(λ + 1))`

Now equate the y component on both the sides,

`(3 - 2λ)/(λ + 1) = 0`

On further simplification,

`λ = 3/2`

So x-axis divides AB in the ratio `3/2`