1. **State the problem:** Find the distance between the points $(8, 7)$ and $(-2, 10)$. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the values:** $$d = \sqrt{(-2 - 8)^2 + (10 - 7)^2}$$ 4. **Calculate the differences:** $$d = \sqrt{(-10)^2 + (3)^2}$$ 5. **Square the differences:** $$d = \sqrt{100 + 9}$$ 6. **Add the squares:** $$d = \sqrt{109}$$ 7. **Final answer:** The distance between the points is $\sqrt{109}$, which is approximately $10.44$.