A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?

Slope of line 2x + 3y = 6 is $$(-\frac{2}{3})$$

Product of slopes of two perpendicular lines = -1

Let slope of line passing through origin = $$m$$

=> $$m \times \frac{-2}{3} = -1$$

=> $$m = \frac{3}{2}$$

Equation of line passing through origin and having slope m is $$y = mx$$    (Since y intercept is zero)

=> $$y = \frac{3}{2} x$$

=> $$3x = 2y$$ 

Solving the above equations, we get the intersection point M = $$(\frac{12}{13} , \frac{18}{13})$$

=> Ans - (A)