1. **State the problem:** Find the distance between the points $(-4, -4)$ and $(6, -6)$ 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: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the coordinates:** $$d = \sqrt{(6 - (-4))^2 + (-6 - (-4))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(6 + 4)^2 + (-6 + 4)^2}$$ $$d = \sqrt{10^2 + (-2)^2}$$ 5. **Calculate the squares:** $$d = \sqrt{100 + 4}$$ 6. **Add the values inside the square root:** $$d = \sqrt{104}$$ 7. **Simplify the square root if possible:** $$104 = 4 \times 26$$ $$d = \sqrt{4 \times 26} = \sqrt{4} \times \sqrt{26} = 2\sqrt{26}$$ 8. **Calculate the decimal value:** $$d \approx 2 \times 5.099 = 10.198$$ 9. **Round to 1 decimal place:** $$d \approx 10.2$$ **Final answer:** The distance between the points is approximately $10.2$ units.