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If $P M$ is the perpendicular from $P(2,3)$ onto the line $x+y=3$, then the coordinates of $M$ are
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Verified Answer
The correct answer is:
(1, 2)
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 $(1,2)$.
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 $(1,2)$.
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