Question

Find the ratio in with the line segment joining the point A(3,-6)and B(5,3) is divided by x-axis

Answer 1

X axis divides the line in the ratio 2:1

Answer 2

Let the point on X-axis be f(x,0) since the y-coordinate is always zero on X-axis.
Given A(2, 3) and B(5, 6)
Let P divides the line segment joining the points (2, 3) and (5, 6) in the ratio m:1

The coordinates of  f=(mx2+x1/m+1,my2+y1/m+1)
Then I put the value of give fourmula

$(x.0) = ( \frac{5m + 5}{m + 1} . \frac{6m + 3}{m + 1} ) \\ \frac{6m + 3}{m + 1} = 0 \\ 6m + 3 = 0 \\ 6m = - 3 \\ m = - \frac{1}{3}$
m:1=> -1/2:1
=> -1:2



Therefore, P divides the line segment joining two points in the ratio 1 : 2 externally.

I hope it's help you