Answer
$${\bf{c}}.\,\left( {3,8} \right)$$
Work Step by Step
$$\eqalign{
& {\text{Using the midpoint rule for all points}} \cr
& {\bf{a}}.\,\left( {1,9} \right) \cr
& \frac{{1 + 9}}{2} = 5 \cr
& {\bf{b}}.\,\left( {4,6} \right) \cr
& \frac{{4 + 6}}{2} = 5 \cr
& {\bf{c}}.\,\left( {3,8} \right) \cr
& \frac{{3 + 8}}{2} = \frac{{11}}{2} = 5.5 \cr
& {\bf{d}}.\,\left( {4.5,5.5} \right) \cr
& \frac{{4.5 + 5.5}}{2} = 5 \cr
& {\text{The answer is }}{\bf{c}}.\,\left( {3,8} \right) \cr} $$
