Check if coordinate in selected area

Question

I have 4 coordinates of area: x1,y1 ... etc. And have one more position x0,y0.

How to check if my coordinate in selected area?

Answer 1

I will explain you how to check that (x0,y0) lies "below" the line through (x1,y1) and (x2,y2). Essentially, you want that the vector (x0-x1,y0-y1) points "to the right" of (x2-x1, y2-y1). This is equivalent to saying that the matrix

x0-x1      y0-y1

x2-x1      y2-y1

has a negative determinant. So your condition becomes

(x0-x1)(y2-y1) < (y0-y1)(x2-x1).

You get such a condition for any line bounding the area.