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

Options

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

Answer

B

Explanation

Clearly , ` x_(1) = (2k+1)/(k+1) and y_(1) = (7k +3)/(k+1)`
Since (`x_(1) ,y_(1))` satisfies the equation 3x +y =9
` 3. ((2k+1)/(k+1)) + ((7k+3)/(k+1)) =9`
` Rightarrow 6k + 3+7k+3 = 9k +9`
` Rightarrow 13k - 9k = 9 -6`
` Rightarrow 4k -3 Rightarrow k = 3/4`
Thus, line 3x+y=9 divides the line segement in the ratio ` 3/4 : 1 ` i.e, 3 : 4 internally.