1. **State the problem:** Find the distance between the points $A(15, -10)$ and $B(15, 22)$. 2. **Formula used:** The distance 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, $x_1 = 15$, $y_1 = -10$, $x_2 = 15$, and $y_2 = 22$. Substitute these values: $$d = \sqrt{(15 - 15)^2 + (22 - (-10))^2} = \sqrt{0^2 + (22 + 10)^2} = \sqrt{0 + 32^2} = \sqrt{1024}.$$ 4. **Simplify:** $$d = 32.$$ 5. **Interpretation:** The distance between the points is 32 units. Since distance is always positive, the answer is 32 units, not negative. **Final answer:** $$\boxed{32\text{ units}}$$