Question

The ratio in which the line $3x+y-9=0$ divides the line segment joining points (1, 3) and (2, 7) is:

• A. 3:4
• B. 2:3
• C. 4:3
• D. 3:2

Answer 1

The correct option is A 3:4

Let point P(a, b)

By Section Formula.

$a=\frac{2k+1}{k+1},b=\frac{7k+3}{k+1}$ this values will satisfy the line $3x+y=9$
$\therefore 3\left(\frac{2k+1}{k+1}\right)+\frac{7k+3}{k+1}=9$
$\frac{6k+3+7k+3}{k+1}=9$
$\therefore 13k+6=9k+9$
$13k-9k=9-6=3$
$4k=3$ $\therefore k=\frac{3}{4}$