question_answer

Find the ratio in which the line \[3x+y-9=0\]divides the segment joining the points (1,3) and (2,7).

A)  \[3:5\]                          

B)  \[3:7\]

C)  \[3:4\]                          

D)  \[4:3\]

Correct Answer: C

Solution :

Let point R(x, y) divides the PQ into \[K:1\]and point R lies on the line \[=3x+y-9=0\]             \[\therefore \,\,\,\,x=\frac{2K+1}{K+1},\,\,\,y=\frac{7K+3}{K+1}\] Put the value of x and y in the equation of line \[3x+y=9\Rightarrow \frac{6K+3+7K+3}{K+1}=9\] \[13\,K+6=9K+9\Rightarrow 4K=3\] \[K=\frac{3}{4}=\,\underline{\mathbf{3:4}}\]