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`