1. **State the problem:** Find the distance between the points $(4, -4)$ and $(9, -2)$ 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 $x$ and $y$ coordinates form the legs of a right triangle. 3. **Substitute the values:** $$d = \sqrt{(9 - 4)^2 + (-2 - (-4))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{5^2 + ( -2 + 4 )^2}$$ $$d = \sqrt{5^2 + 2^2}$$ 5. **Calculate the squares:** $$d = \sqrt{25 + 4}$$ 6. **Add the values inside the square root:** $$d = \sqrt{29}$$ 7. **Find the decimal approximation:** $$d \approx 5.385$$ 8. **Round to the nearest tenth:** $$d \approx 5.4$$ **Final answer:** The distance between the points $(4, -4)$ and $(9, -2)$ is approximately $5.4$ units.