1. **State the problem:** We need to find the midpoint of the line segment AB where A is (1, 4) and B is (7, -2). 2. **Formula for midpoint:** 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 $x_1=1$, $y_1=4$, $x_2=7$, and $y_2=-2$: $$M = \left( \frac{1 + 7}{2}, \frac{4 + (-2)}{2} \right)$$ 4. **Simplify each coordinate:** $$M = \left( \frac{8}{2}, \frac{2}{2} \right)$$ 5. **Calculate the values:** $$M = (4, 1)$$ **Final answer:** The midpoint of AB is at coordinates $(4, 1)$.