Question

The ratio in which the line 2x + y –4 = 0 divides the line segment joining the points A(2,–2) and
B(3, 7) is .

• A. 2:9
• B. 9:2
• C. 2:7
• D. 7:2

Answer 1

The correct option is A 2:9

Let the line 2x+y-4 = 0 intersects the line segment AB at point C and C divides AB in the ratio k : 1.
$\therefore$ Coordinates of C will be
$(\frac{3k+2}{k+1},\frac{7k-2}{k+1})$
Also, point C lies on the line 2x+y-4 = 0, so it must satisfy its equation.
$\Rightarrow 2\left(\frac{3k+2}{k+1}\right)+\left(\frac{7k-2}{k+1}\right)=4\Rightarrow \frac{6k+4+7k-2}{k+1}=4\Rightarrow 13k+2=4k+4\Rightarrow 9k=2\Rightarrow k=\frac{2}{9}$