Find the ratio in which line segment joining the points (2,-3) and (3,1) is divided by x-axis .

Dear student
A2,-3,B(3,1)let the coordinate of point of division be (x,0)Let the ratio be m:nThe required coordinate  =3m+2nm+n,m-3nm+nGiven the y-coordinate=0 (since it cuts the x-axis)Therefore, m-3nm+n=0m=3nmn=31So, the required ratio is 3:1
Regards

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3:1

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From the above question

Let the required ratio be k:1 i.e m:n

Since the line devides the x axis (x,0)

Therefore A(x,0) ; B(2,-3) ; C(3,-1)

On using section formula

y = my2+ny1/m+n

On replacing values
0 = k X 1 + 1 X -3 / k + 1
0 = k - 3 / k + 1
0 = k - 3
k = 3

Hence the required ratio is 3:1
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