Question

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

• A. $\frac{4}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $\frac{4}{3}$

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

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,

So, $3\frac{k+2}{k+1}+\frac{3k+7}{k+1}=9$

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

$\Rightarrow 3k=4$

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

Thus the required ratio is k : 1, i.e., 4 : 3