Given four coordinates that define the corners of an irregular quadrilateral and a point defined by its coordinates, what is the simplest way to determine if the point is within or outside of the quadrilateral?
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Take a look at this wikipedia entry, or an introductory book on computational geometry.
Although the links provided in some sense answer the question, the specific question can be answered without the full force of a point-in-polygon computation. I would recommend this. Compute whether each angle of your quad $(a,b,c,d)$ is convex or reflex. If one is reflex (say $a$), connect it to the opposite vertex $c$. If all are convex, choose any diagaonal; e.g., $(a,c)$. Now you have partitioned your quad into two triangles. Check if your point is in either triangle, by checking if it is left-of-or-on each of its three edges.