Answer:
To find the weighted average of the coordinates given their weights, we can use the formula for the weighted mean, which is:
[tex]\[\text{Weighted Average} = \frac{\sum (x_i \times w_i)}{\sum w_i}\][/tex]
Where [tex]\( x_i \)[/tex] represents the coordinates and [tex]\( w_i \)[/tex] represents the corresponding weights. Let's calculate this for the data you provided:
- Coordinate [tex]\( x_1 = -5 \)[/tex] with weight \( w_[tex]\( w_1 = 1 \)[/tex]1 = 1 \)
- Coordinate \( x_2 = 1 \) with weight \( w_2 = 2 \)
- Coordinate \( x_3 = 3 \) with weight \( w_3 = 3 \)
Using the formula, we have:
\[
\text{Weighted Average} = \frac{(-5 \times 1) + (1 \times 2) + (3 \times 3)}{1 + 2 + 3}
\]
Let's do the calculations.
The weighted average of the coordinates given their weights is \(1.0\).
Step-by-step explanation:
