Question

find the ratio in which the line segment joining the points A (3, - 6) and B (5, 3) is divided by x axis​

Answer 1

let the ratio on which x-axis be cut is k:1

at the point P(x,0)

by section formula

k×3+1×-6\k+1=0

3k-6/k+1=0

3k-6=k+1

2k=7

k=7/2

ratio=7:2

Answer 2

The coordinate of x axis is(x,0)

And the coordinats of A(3,-6) and B(5,3)

Now, the point (x,o) divides the the line segmet into m1:m2

So, using section formula for internal divusion,

X=(m1.-6+m2.3)/(m1+m2), O=(m1.3+m2.5)/(m1+m2)

Taking R.H.S

O=(m1.3+m2.5)/(m1+m2)

M1.3+M2.5=0

M1.3=-M2.5

M1/M2=-5/3

So, the ratio is -5:3