A) \[1:2\]
B) \[2:1\]
C) \[1:3\]
D) \[3:1\]
E) \[3:2\]
Correct Answer: A
Solution :
Let the point of the line divides the line in ratio\[m:1\]. \[\therefore \] Co-ordinate of point is \[\frac{5m+1}{m+1},\frac{7m-1}{m+1}\] lies on \[y+x=4\] \[\Rightarrow \] \[\frac{7m-1+5m+1}{m+1}=4\] \[\Rightarrow \] \[\frac{12m}{m+1}=4\Rightarrow 12m+4m+4\] \[\Rightarrow \] \[12m-4m=4\] \[\Rightarrow \] \[8m=4\] \[\Rightarrow \] \[m=\frac{1}{2}\] \[\therefore \]Required ratio is\[1:2\].
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