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).

Answer 1

Concept:
Application:

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

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