Lets say that we have a 2 dimensional space and have a point $P(x, y)$. If I have an area, lets say the area that is inside these points
$P_1(-1,-1);P_2(-1,1);P_3(1,-1);P_4(1,1);$
and the point $P(\frac{1}{2},\sqrt{2})$,
how can I prove that the point $P$ is inside or outside the area?