Question

The line 2x + y – 4 = 0 divides the line segment joining \(\mathrm{A}(2, -2)\) and \(\mathrm{B}(3, 7)\) in the ratio

Options

• 2 : 3

• 2 : 5

• 2 : 7

• 2 : 9

Answer 1

2 : 9

Explanation:

Let the ratio be \(m : n\).

Substituting the section point into \(2x + y = 4\):

$$\frac{2(3m + 2n) + (7m - 2n)}{m + n} = 4$$

$$\Rightarrow 13m + 2n = 4m + 4n$$

$$\Rightarrow 9m = 2n$$

Hence m : n = 2 : 9.