Explanation

(c)
Let the coordinate of $M$ are $\left( x_{1},y_{1} \right)$
Since, the line $PM$ is perpendicular to the given line $x + y = 3$
$\therefore\ \frac{y_{1} - 3}{x_{1} - 2} \times ( - 1) = - 1$
$\Rightarrow \ y_{1} - 3 = x_{1} - 2$
$\Rightarrow \ x_{1} - y_{1} + 1 = 0$ …(i)
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and also the point lies on the given line.
$\therefore\ x_{1} + y_{1} - 3 = 0$ …(ii)
On solving Eqs. (i) and (ii), we get
$x_{1} = 1,\ \ y_{1} = 2$
$\therefore$ The coordinates of $M$ are (1, 2).