1. **State the problem:** Find the distance between the points $(-10.6, -17.8)$ and $(15.4, 8.1)$. 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. **Calculate the differences:** $$x_2 - x_1 = 15.4 - (-10.6) = 15.4 + 10.6 = 26$$ $$y_2 - y_1 = 8.1 - (-17.8) = 8.1 + 17.8 = 25.9$$ 4. **Substitute into the formula:** $$d = \sqrt{26^2 + 25.9^2}$$ 5. **Calculate squares:** $$26^2 = 676$$ $$25.9^2 = 670.81$$ 6. **Sum the squares:** $$676 + 670.81 = 1346.81$$ 7. **Find the square root:** $$d = \sqrt{1346.81} \approx 36.7$$ 8. **Final answer:** The distance between the points is approximately **36.7 units**.