1. **State the problem:** Find the midpoint of the line segment joining points A(2, -5) and B(6, 3). 2. **Formula:** The midpoint $M$ of a segment with endpoints $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 3. **Apply the formula:** Substitute $x_1=2$, $y_1=-5$, $x_2=6$, and $y_2=3$: $$M = \left( \frac{2 + 6}{2}, \frac{-5 + 3}{2} \right)$$ 4. **Simplify each coordinate:** $$M = \left( \frac{8}{2}, \frac{-2}{2} \right)$$ 5. **Cancel common factors:** $$M = \left( \cancel{\frac{8}{2}}4, \cancel{\frac{-2}{2}}-1 \right)$$ 6. **Final answer:** The midpoint is $M(4, -1)$. This means the point exactly halfway between A and B is at coordinates (4, -1).