1. **State the problem:** Find the distance between points A(1, -2) and B(7, 4) on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ This formula comes from the Pythagorean theorem, where the difference in x-coordinates and y-coordinates form the legs of a right triangle. 3. **Calculate the differences:** $$x_2 - x_1 = 7 - 1 = 6$$ $$y_2 - y_1 = 4 - (-2) = 4 + 2 = 6$$ 4. **Substitute into the formula:** $$d = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72}$$ 5. **Simplify the square root:** $$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$$ 6. **Approximate the decimal value:** $$6\sqrt{2} \approx 6 \times 1.414 = 8.484$$ 7. **Round to the nearest tenth:** $$8.484 \approx 8.5$$ **Final answer:** The distance between cities A and B is approximately **8.5** units.