find the ratio in which the line segment joining the point A(3,-6) and B(5,3) is divided by x axis. also find the coordinate of the point of intersection.

Let the point of division be (x,0) and let the ratio be k:1

By using section formula , we get

(x,0) = (5k+3/k+1 , 3k-6/k+1 )

comparing y coordinateswe get

3k-6/k+1 = 0

3k-6 =0

3k=6

k=2

therefore ratio =2:1

comparing the x coordinates we get

x = 5k+3/k+1

subtituting k=2 ,we get

x=10 +3/2+1

x=13/3

therefore the points of intersection are (13/3 ,0)