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.