A non-rational path

Consider R^2 - the Euclidean plane consisting of 2-tuples of real numbers. Remove all the points that have rational co-ordinates from it. For example (1/4, 5/100) should be removed, (1/2, sqrt(7)) should NOT be removed. We are left with what is denoted R^2 - Q^2; Q being the rational points. Pick any two points a and b in R^2 - Q^2. Is it possible to find a path (a line - not nessesarily straight) from a and b in R^2 - Q^2?

If the answer is yes, give a precise path and if the answer is no, why?