Question

The line 3x + y = 9 divides line segment joining the points A (2, 7) and B (1, 3) in the ratio of ________ .

• A. 4 : 3
• B. 2 : 3
• C. 1 : 3
• D. 3 : 4

Answer 1

The correct option is A 4 : 3

Let P(x, y) be the point which lies on the line representing 3x + y = 9 and dividing AB in the ratio k : 1.

We know that the coordinates of the point P that divides a line segment in the ratio m : n is given by

$P(x,y)=(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

where, $(x_1,y_1)and(x_2,y_2)$ are the coordinates of the endpoints of the line segment.

So, $x=\frac{k\times 1+1\times 2}{k+1}=\frac{k+2}{k+1}$

and $y=\frac{k\times 3+1\times 7}{k+1}=\frac{3k+7}{k+1}$

Thus point P is $(\frac{k+2}{k+1},\frac{3k+7}{k+1})$

As P lies on 3x + y = 9,

$3\left[\frac{k+2}{k+1}\right]+\frac{3k+7}{k+1}=9$

$\Rightarrow 3k+6+3k+7=9k+9$

$\Rightarrow 3k=4$

$\Rightarrow k=\frac{4}{3}$

Thus, the required ratio is 4 : 3.