In what ratio, the line joining `(1, 1)`and `(5, 7)`is divided by the line `x+y=4`?

Explanation

Let the straight line divides the line segment `A(-1,1)` and `B(5,7)` at a point `P(h,k)` in the ratio `lambda : 1`.

` :. H=(lambda(5)+1(-1))/(lambda+1)=(5lambda-1)/(lambda+1)`
and `k=(lambda(7)+1(1))/(lambda+1)=(7lambda+1)/(lambda+1)`
The point `(h,k)` lies on the line `x+y=4`
`:. h+k=4`
`implies (5lambda-1)/(lambda+1)+(7lambda+1)/(lambda+1)=4`
`implies 5lambda-1+7lambda+1=4lambda+4`
`implies 8lambda=4`
`implies lambda=(1)/(2)`
Therefore, given line divides the line segment `AB` in the ratio `1 : 2`.