Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division.

#### Solution

Solution:

Point p lies on x axis so it’s ordinate is 0 (Using section formula)

Let the ratio be k: 1 Let the coordinate of the point be P(x , 0) As given A(3,-3) and B(-2,7)

The co-ordinates of the point P(x,y), which divide the line segment joining the points A(x_{1},y_{1}) and B(x_{2},y_{2}), internally in the ratio m_{1}:m_{2} are

`P_x=(mx_2+nx_1)/(m+n)`

`P_y=(my_2+ny_1)/(m+n)`

Hence, A(3,-3) be the co-ordinates (x_{1},y_{1}) and B(-2,7) be the co-ordinates (x_{2},y_{2})

m = k

n = 1

0 = k x 7 + 1 x -3 / (k+1)

0(k+1) =7k -3

0 =7k - 3

3=7k

k = 3 /7

k:1 = 3 : 7

`P_x=(mx_2+nx_1)/(m+n)`

`P_x=[(3/7xx-2)+(1xx3)]/(3/7+1)=2.41`