Question

in what ratio x-y-2=0 divides the line segment joining points A(3,-1) and C(0,2)​

Answer 1

Hi Army Girl

Will you be my friend.

Let A(3,-1) and B(8,9).

Let the line x−y−2=0 divide the line segment AB at point C(x,y) in the ratio m:n.

By section formula,

C(x,y)=[ m+nm×8+n×3, m+n,m×9+n×−1 ]

C(x,y)= [ m+n8m+3n, m+n9m−n ]

Since, point C lie on the line x−y−2=0,

8m+3n 9m-n

———— – ———— –2 = 0

m+n m+n

8m+3n−9m+n−2m−2n=0

3m=2n

m 2

—— = —

n 3