If $P M$ is the perpendicular from $P(2,3)$ onto the line $x+y=3$, then the coordinates of $M$ are

Question

Aicharya · Accepted Answer

Let the co-ordinates of $M$ are $\left(x_1, y_1\right)$. Since the line $P M$ is $\perp$ to the given line $x+y=3$

$\begin{aligned} & \therefore \quad \frac{y_1-3}{x_1-2} \times(-1)=1 \\ & \Rightarrow \quad y_1-3=x_1-2 \\ & \end{aligned}$

and also the points lies on the given line

On solving Eqs. (i) and (ii), we get $\therefore \quad x_1=1, y_1=2$ $\therefore$ The co-ordinates of $M$ are $(1,2)$.

Solution