How to determine if a point is within a quadrilateral

If the aim is to code your own test, then pick any classic point in polygon test to implement. Otherwise do what Jacob suggests.

Use inpolygon. Usage would be inpolygon(xt,yt,[x1 x2 x3 x4],[y1 y2 y3 y4])

You can test the Point with this condition. Also you can treat quadrilateral as 2 triangles to calculate its area.

Since it's a simple quadrilateral you can test for a point in triangle for each end and a point in rectangle for the middle.

EDIT Here is some pseudo code for point in triangle:

function SameSide(p1,p2, a,b)
    cp1 = CrossProduct(b-a, p1-a)
    cp2 = CrossProduct(b-a, p2-a)
    if DotProduct(cp1, cp2) >= 0 then return true
    else return false

function PointInTriangle(p, a,b,c)
    if SameSide(p,a, b,c) and SameSide(p,b, a,c)
        and SameSide(p,c, a,b) then return true
    else return false

Or using Barycentric technique:

A, B, and C are the triangle end points, P is the point under test

// Compute vectors        
v0 = C - A
v1 = B - A
v2 = P - A

// Compute dot products
dot00 = dot(v0, v0)
dot01 = dot(v0, v1)
dot02 = dot(v0, v2)
dot11 = dot(v1, v1)
dot12 = dot(v1, v2)

// Compute barycentric coordinates
invDenom = 1 / (dot00 * dot11 - dot01 * dot01)
u = (dot11 * dot02 - dot01 * dot12) * invDenom
v = (dot00 * dot12 - dot01 * dot02) * invDenom

// Check if point is in triangle
return (u > 0) && (v > 0) && (u + v < 1)