A) \[2:1\]
B) \[1:2\]
C) \[2:3\]
D) \[3:2\]
Correct Answer: B
Solution :
[b] Let p be a point on the line\[x+y=4\], which divide the line joining \[A\left( -1,1 \right)\]and\[B\left( 5,7 \right)\]. P divide the line joining A and B be \[\lambda :1\] \[\therefore P\equiv \left( \frac{5\lambda +(-1)}{\lambda +1}.\frac{7\lambda +1}{\lambda +1} \right)\] Now, \[x+y=4\] \[\therefore \frac{5\lambda -1}{\lambda +1}=\frac{7\lambda +1}{\lambda +1}=4\] \[\Rightarrow 5\lambda +7\lambda -1+1=4\left( \lambda +1 \right)\] \[8\lambda =4\] \[\lambda =\frac{1}{2}=1:2\] Hence, option [b] is correct.
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