Given that (m) is the midpoint of (ab), (q) is the midpoint of (am), and (t) is the midpoint of the coordinates of (a) and (b), find the coordinates of (aq) and (t) in most simplified terms.

a. (aq = a + b/2, t = a + b/2)
b. (aq = a + m/2, t = a + b/2)
c. (aq = a + m/2, t = m + b/2)
d. (aq = m + b/2, t = a + b/2)