A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find the co-ordinates of M.

Solution (By Examveda Team)

Equation of line perpendicular to line 3x - 2y = 6 is 2x + 3y + p = 0

As, the line passes through origin (0, 0)
∴ 2 × 0 + 3 × 0 + p = 0
∴ p = 0
Now, the equation is 2x + 3y = 0
∴ 2x = -3y
x = $$\frac{{ - 3}}{2}$$ y
By putting this value in equation 3x - 2y = 6
$$\eqalign{ & \Rightarrow 3\left( {\frac{{ - 3}}{2}} \right)y - 2y = 6 \cr & \Rightarrow \frac{{ - 9}}{2}y - 2y = 6 \cr & \Rightarrow \frac{{ - 13y}}{2} = 6 \cr & \Rightarrow y = - \frac{{12}}{{13}} \cr & \therefore x = \frac{{ - 3}}{2} \times \left( {\frac{{ - 12}}{{13}}} \right) \cr & x = \frac{{18}}{{13}} \cr & \therefore {\text{Co - ordinate of point}} \cr & {\text{M}} = \left[ {\frac{{18}}{{13}},\, - \frac{{12}}{{13}}} \right] \cr} $$