Henry decides one morning to do a workout, and he walks \dfrac{3}{4} of the way from his home to his gym. The gym is 2 kilometers away from Henry’s home. At that point, he changes his mind and walks \dfrac{3}{4} of the way from where he is back toward home. When he reaches that point, he changes his mind again and walks \dfrac{3}{4} of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked \dfrac{3}{4} of the distance toward either the gym or home from the point where he last changed his mind, he will get very close to walking back and forth between a point A kilometers from home and a point B kilometers from home. What is |A-B| ?

**Answer Choices**

A. \dfrac{2}{3}

B. 1

C. 1 \dfrac{1}{5}

D. 1 \dfrac{1}{4}

E. 1 \dfrac{1}{2}