For example, consider one line segment from (x,0,z) to (x,y,z), and another from (x,0,2z) to (x,y,2z).  These are the same length. 
These project in the image to a line from (fx/z,0) to (fx/z, fy/z) and from (fx/z,0) to  (fx/2z, fy/2z), where we can rewrite the last point as: (1/2)(fx/z,fy/z).  The second line is half as long as the first.