1. **State the problem:** Given points A(-3, 7) and B(5, -2), find the length of the line segment AB and the midpoint of AB. 2. **Length of the line segment formula:** $$d_{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where $A(x_1, y_1) = (-3, 7)$ and $B(x_2, y_2) = (5, -2)$. 3. **Calculate the differences:** $$x_2 - x_1 = 5 - (-3) = 5 + 3 = 8$$ $$y_2 - y_1 = -2 - 7 = -9$$ 4. **Substitute into the distance formula:** $$d_{AB} = \sqrt{8^2 + (-9)^2} = \sqrt{64 + 81} = \sqrt{145}$$ 5. **Simplify the square root:** $$\sqrt{145} \approx 12.04$$ 6. **Midpoint formula:** The midpoint $M$ of segment $AB$ is given by: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 7. **Calculate midpoint coordinates:** $$x_M = \frac{-3 + 5}{2} = \frac{2}{2} = 1$$ $$y_M = \frac{7 + (-2)}{2} = \frac{5}{2} = 2.5$$ 8. **Final answer:** - Length of segment $AB$ is approximately $12.04$ units. - Midpoint of segment $AB$ is $M(1, 2.5)$.