Final answer:
The weighted average of points A, B, and C is (6, -2/3), calculated by multiplying each point by its weight and summing these products, then dividing by the sum of the weights.
Step-by-step explanation:
The question asks for the weighted average of three points A, B, and C with respective weights 3, 1, and 2. To find the weighted average, we multiply each point by its weight and then divide by the sum of the weights.
The calculation for the weighted average (W) is:
W = (Weight_A × Point_A + Weight_B × Point_B + Weight_C × Point_C) / (Weight_A + Weight_B + Weight_C)
Given the points: A = (7,2), B = (1,6), and C = (7,-8), and their weights: Weight_A = 3, Weight_B = 1, and Weight_C = 2, the calculation becomes:
W = ((3 × 7 + 1 × 1 + 2 × 7) / (3+1+2), (3 × 2 + 1 × 6 + 2 × -8) / (3+1+2))
For the x-coordinate:
Wx = (3 × 7 + 1 × 1 + 2 × 7) / 6 = (21 + 1 + 14) / 6 = 36 / 6 = 6
For the y-coordinate:
Wy = (3 × 2 + 1 × 6 + 2 × -8) / 6 = (6 + 6 - 16) / 6 = -4 / 6 = -2/3
Therefore, the weighted average of the points A, B, and C is (6, -2/3).