There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is the center of the square. Given that point Q is randomly chosen from among the other 80 points, what is the probability that line PQ is a line of symmetry for the square?
[asy]
size(130);
defaultpen(fontsize(11));
int i, j;
for(i=0; i<9; i=i+1)
{
for(j=0; j<9; j=j+1)
if((i==4) && (j==4))
{
dot((i,j),linewidth(5));
} else {
dot((i,j),linewidth(3));
}
}
dot("P",(4,4),NE);
draw((0,0)--(0,8)--(8,8)--(8,0)--cycle);
[/asy]
<spanclass=′latex−bold′>(A)</span>51<spanclass=′latex−bold′>(B)</span>41<spanclass=′latex−bold′>(C)</span>52<spanclass=′latex−bold′>(D)</span>209<spanclass=′latex−bold′>(E)</span>21