Two particles move along the edges of equilateral \triangle A B C in the direction
A \rightarrow B \rightarrow C \rightarrow A
starting simultaneously and moving at the same speed. One starts at A, and the other starts at the midpoint of \overline{B C}. The midpoint of the line segment joining the two particles traces out a path that encloses a region R. What is the ratio of the area of R to the area of \triangle A B C ?
Answer Choices
A. \dfrac{1}{16}
B. \dfrac{1}{12}
C. \dfrac{1}{9}
D. \dfrac{1}{6}
E. \dfrac{1}{4}