1. **State the problem:** We need to find the weighted average of points A, B, and C on a number line where point B weighs twice as much as point A, and point C weighs twice as much as point A. 2. **Identify the points and weights:** - Point A is at $-5$ with weight $w_A = 1$ (let's assign this as the base weight). - Point B is at $-4$ with weight $w_B = 2 \times w_A = 2$. - Point C is at $2$ with weight $w_C = 2 \times w_A = 2$. 3. **Formula for weighted average:** $$\text{Weighted Average} = \frac{w_A x_A + w_B x_B + w_C x_C}{w_A + w_B + w_C}$$ 4. **Substitute values:** $$= \frac{1 \times (-5) + 2 \times (-4) + 2 \times 2}{1 + 2 + 2}$$ 5. **Calculate numerator:** $$= \frac{-5 - 8 + 4}{5}$$ 6. **Simplify numerator:** $$= \frac{-9}{5}$$ 7. **Calculate weighted average:** $$= -1.8$$ **Final answer:** The weighted average of points A, B, and C is $-1.8$.