Final answer:
The weighted average of the points A(4,3) with a weight of 1, B(-8,-4) with a weight of 1, and C(1,2) with a weight of 2, is calculated by summing the products of the coordinates with their respective weights and then dividing by the sum of weights, resulting in a weighted average point of (-0.5, 0.75).
Step-by-step explanation:
To find the weighted average of the points A(4,3) with a weight of 1, B(-8,-4) with a weight of 1, and C(1,2) with a weight of 2, we use the following formula:
- The weighted average of the x-coordinates: (Sum of weighted x-coordinates) / (Sum of weights)
- The weighted average of the y-coordinates: (Sum of weighted y-coordinates) / (Sum of weights)
For the x-coordinates:
(4×1 + (-8)×1 + 1×2) / (1 + 1 + 2) = (4 - 8 + 2) / 4 = -2 / 4 = -0.5
For the y-coordinates:
(3×1 + (-4)×1 + 2×2) / (1 + 1 + 2) = (3 - 4 + 4) / 4 = 3 / 4 = 0.75
The weighted average of the points is (-0.5, 0.75).