If PM is the perpendicular from P ( 2,  3) on to the line x + y = 3 then M =

:   m = (h,  k)  be the foot of perpendicular from P (2,  3) = ( x₁,  y₁) on to the line x + y – 3 = 0

$\begin{array}{l}\therefore \frac{h-2}{1}=\frac{k-3}{1}=\frac{-\left(2+3-3\right)}{1+1}\\ \Rightarrow \frac{h-2}{1}=\frac{k-3}{1}=-1\\ h-2=-1,k-3=-1\\ h=-1+2\Rightarrow 1,k=-1+3\Rightarrow 2\\ \therefore m=\left(1,2\right)\end{array}$