Step 1: Use the midpoint formula
The midpoint \( M \) of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Step 2: Substitute the given points
Let \( (x_1, y_1) = (-1, 3) \) and \( (x_2, y_2) = \left(8, \frac{3}{2} \right) \)
Step 3: Calculate the x-coordinate of the midpoint
\[
\frac{-1 + 8}{2} = \frac{7}{2}
\]
Step 4: Calculate the y-coordinate of the midpoint
\[
\frac{3 + \frac{3}{2}}{2} = \frac{\frac{6}{2} + \frac{3}{2}}{2} = \frac{\frac{9}{2}}{2} = \frac{9}{4}
\]
Final Answer:
\[
\left( \frac{7}{2}, \frac{9}{4} \right)
\]