SOLUTION
Consider the image:
Notice that the line KP will be perpendicular to the line LM
The slope of LM is:
[tex]\begin{gathered} m=\frac{8-2}{3-(-2)} \\ m=\frac{6}{5} \end{gathered}[/tex]
since the line KP is perpendicular to line LM then the slope of LM is:
[tex]\begin{gathered} n=-\frac{1}{\frac{6}{5}} \\ m=-\frac{5}{6} \end{gathered}[/tex]
Since line KP passes through the point K(3,3) then the equation is:
[tex]\begin{gathered} y-3=-\frac{5}{6}(x-3) \\ y=-\frac{5}{6}x+\frac{11}{2} \end{gathered}[/tex]
Similarly the the equation of line LM is:
[tex]\begin{gathered} y-8=\frac{6}{5}(x-3) \\ y=\frac{6}{5}x+\frac{22}{5} \end{gathered}[/tex]
Therefore the coordinates of P is:
[tex](0.541,5.049)[/tex]
