1. **State the problem:** Find the midpoint of the line segment joining the points $(-1, -3)$ and $(-3, 14)$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 3. **Substitute the given points:** $$M = \left( \frac{-1 + (-3)}{2}, \frac{-3 + 14}{2} \right)$$ 4. **Simplify the sums:** $$M = \left( \frac{-4}{2}, \frac{11}{2} \right)$$ 5. **Simplify the fractions:** $$M = \left( \cancel{\frac{-4}{2}} \to -2, \cancel{\frac{11}{2}} \to \frac{11}{2} \right)$$ 6. **Final answer:** The midpoint is $\boxed{(-2, \frac{11}{2})}$.