Rectangle A B C D has A B=5 and B C=4. Point E lies on \overline{A B} so that E B=1, point G lies on \overline{B C} so that C G=1, and point F lies on \overline{C D} so that D F=2. Segments \overline{A G} and \overline{A C} intersect \overline{E F} at Q and P, respectively. What is the value of \dfrac{P Q}{E F} ?
Answer Choices
A. \dfrac{\sqrt{3}}{16}
B. \dfrac{\sqrt{2}}{13}
C. \dfrac{9}{82}
D. \dfrac{10}{91}
E. \dfrac{1}{9}