1. **State the problem:** Find the distance between points $M(5, -6)$ and $N(-3, -10)$ rounded to the nearest tenth. 2. **Formula:** The distance $d$ 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 the coordinates:** $$d = \sqrt{(-3 - 5)^2 + (-10 - (-6))^2}$$ $$d = \sqrt{(-8)^2 + (-4)^2}$$ 4. **Calculate squares:** $$d = \sqrt{64 + 16}$$ 5. **Sum inside the square root:** $$d = \sqrt{80}$$ 6. **Simplify the square root:** $$d = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$ 7. **Approximate the value:** $$d \approx 4 \times 2.236 = 8.944$$ 8. **Round to the nearest tenth:** $$d \approx 8.9$$ **Final answer:** The distance between points $M$ and $N$ is approximately **8.9 units**.