1. **State the problem:** Find the distance between the points $(2, -4)$ and $(2, 3)$. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the formula:** Here, $x_1 = 2$, $y_1 = -4$, $x_2 = 2$, and $y_2 = 3$. 4. Calculate the differences: $$x_2 - x_1 = 2 - 2 = 0$$ $$y_2 - y_1 = 3 - (-4) = 3 + 4 = 7$$ 5. Substitute into the distance formula: $$d = \sqrt{0^2 + 7^2} = \sqrt{0 + 49} = \sqrt{49}$$ 6. Simplify the square root: $$d = 7$$ **Final answer:** The distance between the points $(2, -4)$ and $(2, 3)$ is $7$.