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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. - Mathematics

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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.

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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(x1,y1) and B(x2,y2), internally in the ratio m1:m2 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 (x1,y1) and B(-2,7) be the co-ordinates (x2,y2)
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`

Concept: Division of a Line Segment
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