1. **State the problem:** Find the distance between the two points $(4, 5)$ and $(-3, -2)$ 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. **Calculate the differences:** $$x_2 - x_1 = -3 - 4 = -7$$ $$y_2 - y_1 = -2 - 5 = -7$$ 4. **Square the differences:** $$(-7)^2 = 49$$ $$(-7)^2 = 49$$ 5. **Sum the squares:** $$49 + 49 = 98$$ 6. **Take the square root:** $$d = \sqrt{98}$$ 7. **Simplify the radical:** Since $98 = 49 \times 2$, and $\sqrt{49} = 7$, we have: $$d = 7\sqrt{2}$$ **Final answer:** The distance between the points is $7\sqrt{2}$.