Question

in what ratio does the line x+y-1=0 divide the line segment joining the point A(3,3) and the origin .​

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In what ratio does the line x−y−2=0 divide the line segment joining the points(3,−1) and (8,9)? Also, find co-ordinates of point of intersection. 

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ANSWER

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+nm×9+n×−1]

C(x,y)=[m+n8m+3n,m+n9m−n]

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

m+n8m+3n−m+n9m−n−2=0

8m+3n−9m+n−2m−2n=0

3m=2n

nm=32

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