There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that point Q is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?
Answer Choices
A. \dfrac{1}{5}
B. \dfrac{1}{4}
C. \dfrac{2}{5}
D. \dfrac{9}{20}
E. \dfrac{1}{2}