Points, Lines & Planes · Superchallenge problem

Pentagon $ABCDE$ has the following side midpoints: the midpoint of $\overline{AB}$ is $(2, 1)$, of $\overline{BC}$ is $(5, 3)$, of $\overline{CD}$ is $(6, 7)$, of $\overline{DE}$ is $(2, 8)$, and of $\overline{EA}$ is $(0, 4)$. Find the coordinates of vertex $A$.