Question

Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.

Answer 1

Let C(x, 0) divides the line-segment A(1, –3) and B(4, 5) in k : 1 ratio.
By section formula,

`(x, y ) = ((mx_2 + nx_1)/(m+n), (my_2 + ny_2)/(m +n))`

⇒ `(x,0) = ((4k + 1xx1)/(k + 1) , (5k + 1 xx (-3))/(k + 1))`

⇒ `(x , 0) = ((4k + 1)/(k + 1) , (5k - 3)/(k + 1))`

⇒ `(5k - 3)/(k + 1) = 0`

⇒ `5k - 3 = 0`

⇒ `5k = 3`

⇒ `k = (3)/(5)`

and `x = (4k + 1)/(k + 1) = (4 xx (3)/(5) +1)/((3)/(5)+1)`

⇒ `x = ((12+5)/(5))/((3+5)/(5))`

⇒ `x =  (17)/(8)`

The ratio in which C divides A and B is k : 1 i.e., 3 : 5 and the coordinate of C is `((17)/(8) , 0)`.