Question

The line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B (3, 7) in the ratio

(a) 2 : 5 (b) 2 : 9 (c) 2 : 7 (d) 2 : 3

Answer 1

Let us assume the line divides AB in k: 1 ratio.

Coordinates of the the point of division can be given as follows:

$x=\frac{2+3k}{k+1}y=\frac{-2+7k}{k+1}$

Substituting the values of x and y in the the following equation;

$2x+y-4=02\left(\frac{2+3k}{k+1}\right)+\left(\frac{-2+7k}{k+1}\right)-4=0\frac{4+6k}{k+1}+\left(\frac{-2+7k}{k+1}\right)-4=04+6k-2+7k-4(k+1)=04+6k-2+7k-4k-4=0-2+9k=09k=2k=\frac{2}{9}$

Hence, the ratio is 2: 9.

(b) 2:9 is the correct answer