Question

Determine the ratio in which the line $2x+y=4$ divides the line segment joining the points A(2,-2) and B(3, 7).

• A. 2 : 9
• B. 4 : 5
• C. 5 : 4
• D. 2 : 3

Answer 1

The correct option is A 2 : 9

Given, A(2,-2) and B(3,7).
Let, the point P divide the line in the ratio k : 1.

By section formula,
The coordinates of P are
$(\frac{3\times k+1\times 2}{k+1},\frac{k\times 7+1\times -2}{k+1})=(\frac{3k+2}{k+1},\frac{7k-2}{k+1})$

Now, this point lies on the line $2x+y=4$

Hence,
$2\times \frac{3k+2}{k+1}+\frac{7k-2}{k+1}=4$

$\Rightarrow 2(3k+2)+(7k-2)-4(k+1)=0$

$\Rightarrow (6k+4+7k-2-4k-4=0$

$\Rightarrow 9k-2=0$.

$\Rightarrow k=\frac{2}{9}$

$\Rightarrow k:1=2:9$