Question

find the coordinates of p that represent the weighted average for the given set of points with the given weights.

• a has a weight of 3.
• b has a weight of 2.

Explanation:

Step1: Calculate the \(x\) - coordinate of \(P\)

Use the formula \(x=\frac{w_1x_1 + w_2x_2}{w_1 + w_2}\), where \(w_1 = 3\), \(x_1=-1\), \(w_2 = 2\), \(x_2 = 3\).

$$x=\frac{3\times(-1)+2\times3}{3 + 2}=\frac{-3 + 6}{5}=\frac{3}{5}=0.6$$

Step2: Calculate the \(y\) - coordinate of \(P\)

Use the formula \(y=\frac{w_1y_1+w_2y_2}{w_1 + w_2}\), where \(w_1 = 3\), \(y_1 = 1\), \(w_2=2\), \(y_2 = 9\).

$$y=\frac{3\times1+2\times9}{3 + 2}=\frac{3+18}{5}=\frac{21}{5}=4.2$$

Answer:

\(P=(0.6,4.2)\)