Question

Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) 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 (3,−6) and B (5, 3) 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 ) = ((5λ + 3 ) /(λ + 1 ) , ( 3λ - 6)/(λ + 1))`

Now equate the y component on both the sides,

`(3λ - 6 ) / (λ + 1 )=0`

On further simplification,

`λ = 2/1`

So x-axis divides AB in the ratio 2:1.