TITLE: Determine if the coordinates of a point are within an irregular quadrilateral whose corners are defined by coordinates
QUESTION [6 upvotes]: 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?

REPLY [4 votes]: 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.