1. **Problem:** Find the distance between points $A(0,0)$ and $B(3,4)$. 2. **Formula:** 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. **Apply the formula:** Substitute $x_1=0$, $y_1=0$, $x_2=3$, and $y_2=4$: $$d = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{3^2 + 4^2}$$ 4. **Calculate squares:** $$d = \sqrt{9 + 16}$$ 5. **Sum inside the root:** $$d = \sqrt{25}$$ 6. **Square root:** $$d = 5$$ 7. **Answer:** The distance between points $A$ and $B$ is 5. **Final answer:** A. 5