1. **State the problem:** Find the distance between points $A(2,5)$ and $B(4,9)$ using the distance formula. 2. **Distance formula:** The distance $d$ between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the coordinates:** $$d = \sqrt{(4 - 2)^2 + (9 - 5)^2}$$ 4. **Calculate the differences:** $$d = \sqrt{2^2 + 4^2}$$ 5. **Square the differences:** $$d = \sqrt{4 + 16}$$ 6. **Add the squares:** $$d = \sqrt{20}$$ 7. **Simplify the square root:** $$d = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$$ **Final answer:** The distance between points $A$ and $B$ is $2\sqrt{5}$.