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

Options

A. 3:4 externally
B. 3:4 internally
C. 4:5 internally
D. 5:6 externally

Answer

B

Explanation

`becausex_(1)=(2k+1)/(k+1) and y_(1)=(7k+3)/(k+1)`
So, `(x_(1),y_(1))` satisfies the equation `3x+y=g`.
Now, `3*((2k+1)/(k+1))+((7k+3)/(k+1))=9`
`implies6k+3+7k+3=9k+9`
`implies13k-9k=9-6`
`implies4k=3`
`impliesk=(3)/(4)`
So, line 3x+y=9 divides the line segment in the ratio `(3)/(4):1`
i.e., 3:4 internally.