Final answer:
The weighted average of points A (3,3), B (-8,-5), and C (-8,2) with weights 1, 4, and 1, respectively, is calculated by multiplying each point by its weight, summing them up, and then dividing by the total weight. The resulting weighted average is approximately (-6.17, -2.50).
Step-by-step explanation:
To calculate the weighted average of points A, B, and C with respective weights 1, 4, and 1, we do the following:
- First, multiply each point by its corresponding weight: (A × 1), (B × 4), and (C × 1).
- For point A with coordinates (3,3), the weighted point will be (3 × 1, 3 × 1) = (3, 3).
- For point B with coordinates (-8, -5), the weighted point will be (-8 × 4, -5 × 4) = (-32, -20).
- For point C with coordinates (-8, 2), the weighted point will be (-8 × 1, 2 × 1) = (-8, 2).
- Add the weighted points: (3 - 32 - 8, 3 - 20 + 2) = (-37, -15).
- Finally, divide each coordinate sum by the total weight, which is 1 + 4 + 1 = 6, to get the average: (-37/6, -15/6).
The weighted average of the points is (-37/6, -15/6), which simplifies to approximately (-6.17, -2.50).