1. **State the problem:** Find the distance $d$ between points $A(-5,5)$ and $B(5,-5)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute values:** $$d = \sqrt{(5 - (-5))^2 + (-5 - 5)^2}$$ 4. **Simplify inside parentheses:** $$d = \sqrt{(5 + 5)^2 + (-10)^2}$$ 5. **Calculate powers:** $$d = \sqrt{10^2 + (-10)^2} = \sqrt{100 + 100}$$ 6. **Add inside the square root:** $$d = \sqrt{200}$$ 7. **Simplify the square root:** $$d = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$$ 8. **Approximate and round to nearest tenth:** $$d \approx 10 \times 1.414 = 14.14 \approx 14.1$$ **Final answer:** $$d = 14.1$$