1. **State the problem:** Find the coordinates of the midpoint of the line segment joining the points $(4, -11)$ and $(-2, 7)$. 2. **Formula for midpoint:** The midpoint $M$ of a line segment joining points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ This formula calculates the average of the $x$-coordinates and the average of the $y$-coordinates. 3. **Apply the formula:** $$M = \left( \frac{4 + (-2)}{2}, \frac{-11 + 7}{2} \right)$$ 4. **Simplify the numerator:** $$M = \left( \frac{4 - 2}{2}, \frac{-11 + 7}{2} \right)$$ 5. **Calculate the sums:** $$M = \left( \frac{2}{2}, \frac{-4}{2} \right)$$ 6. **Simplify the fractions:** $$M = \left( \cancel{\frac{2}{2}}1, \cancel{\frac{-4}{2}}-2 \right)$$ 7. **Final answer:** The midpoint is at coordinates $\boxed{(1, -2)}$. This means the point exactly halfway between $(4, -11)$ and $(-2, 7)$ is $(1, -2)$.