In order to turn this process into a correlation, the Euclidean plane (which is not a projective plane) needs to be expanded to the extended euclidean plane by adding a line at infinity and points at infinity which lie on this line. In this expanded plane, we define the polar of the point to be the line at infinity (and is the pole of the line at infinity), and the poles of the lines through are the points of infinity where, if a line has slope its pole is the infinite point associated to the parallel class of lines with slope . The pole of the -axis is the point of infinity of the vertical lines and the pole of the -axis is the point of infinity of the horizontal lines.