Question

in what ratio is the line joining the points (4,3) and (-10,-4) divided by x axis? also find the coordinates of point of intersection.

Answer 1

The line segment joining two points A(4,3) and B (-10,-4) is divided by x axis

Let Point of Intersection between AB be P (x,y)

Let the divided ratio be m : n  

x = m*4+n*-10 / m+n    i>                y = m*3+ n*- 4 / m+n  ii>

As the Two points And B lies over x- axis and are divided by x - axis

Then the y- intercept = 0 then, putting y = 0 in ii> we get

0 = 3m- 4n/m+n

3m - 4n= 0

3m = 4n

m/n = 4/3

m : n = 4 : 3

Then the point of intersection of the line segment AB (y =0 )

From i> we get

x = 4*4 - 10 *3/4+3

x = 16 - 30 / 7

x = - 14/7

x = -2

The Coordinates of the point of intersection P are ( - 2, 0)

Answer 2

Please see the attachment