1. **State the problem:** Find the distance between points $C(-9, 2)$ and $D(-7, 5)$ on the Cartesian 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 coordinates:** $$d = \sqrt{(-7 - (-9))^2 + (5 - 2)^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(-7 + 9)^2 + (3)^2}$$ $$d = \sqrt{(2)^2 + 3^2}$$ 5. **Calculate the squares:** $$d = \sqrt{4 + 9}$$ 6. **Add the values:** $$d = \sqrt{13}$$ 7. **Final answer:** The distance between points $C$ and $D$ is $$\boxed{\sqrt{13}}$$ units. This means the straight-line distance between the two points is the square root of 13, approximately 3.6 units.