1. **State the problem:** Find the distance between the points $(-6, -3)$ and $(4, -7)$ using Pythagoras' theorem. 2. **Formula:** 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. **Calculate the differences:** $$x_2 - x_1 = 4 - (-6) = 4 + 6 = 10$$ $$y_2 - y_1 = -7 - (-3) = -7 + 3 = -4$$ 4. **Substitute into the formula:** $$d = \sqrt{10^2 + (-4)^2} = \sqrt{100 + 16} = \sqrt{116}$$ 5. **Simplify the square root:** $$d = \sqrt{116} = \sqrt{4 \times 29} = 2\sqrt{29}$$ 6. **Calculate the decimal value:** $$d \approx 2 \times 5.385 = 10.770$$ 7. **Round to 1 decimal place:** $$d \approx 10.8$$ **Final answer:** The distance between the points is approximately **10.8 units**.