Count points in a rectangle

Question

I have lots (billions) of points in 2D which I can preprocess and I would like to answer queries which are of the following form:

Given all four corners of a rectang

Answer 1

Make triangle. Suppose, abcd is the rectangle and x is the point then if area(abx)+area(bcx)+area(cdx)+area(dax) equals area(abcd) then the point is inside it.