1. **State the problem:** We need to find the distance between two points $A(1, 9)$ and $B(-4, -3)$ in 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: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the coordinates:** $$d = \sqrt{(-4 - 1)^2 + (-3 - 9)^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(-5)^2 + (-12)^2}$$ 5. **Square the values:** $$d = \sqrt{25 + 144}$$ 6. **Add the squares:** $$d = \sqrt{169}$$ 7. **Calculate the square root:** $$d = 13$$ **Final answer:** The distance between points A and B is $13.0$ units.