I misunderstood your problem. I presumed you were using an isometric transformation to go from world to view space. I also presumed the random point you wanted to check was a point in view space.
However, my original answer can actually be used to provide a speedy solution to your actual problem. Even though it probably will be slower than using the built-in point-in-triangle functions, I'll write this out just because I'm embarrassed about misunderstanding the nature of your problem.
View attachment 27023
Let's say p0 is one of the points of the quadrilateral.
And p1, p2 are two other points at the end of the sides coming off of p0.
And that p3 is the point you want to check.
If (a,b) is p1-p0, and (c,d) is p2-p0. and (x0,y0) is p3-p0.
Then you can can check if the point is in that quadrilateral like this:
var _id = 1 /(a*d-b*c);
var x1 = ( x0*d - y0*c) * _id;
var y1 = (-x0*b + y0*a) * _id;
var in_quad = (x1 > 0) and (y1 > 0) and (x1 < 1) and (y1 < 1);