Question

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

• 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

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

Or 3k + 6 + 3k + 7 = 9k + 9

Or 3k = 4

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

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