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 1.
• b has a weight of 2.

a(-5,6)
b(-1,-2)

Explanation:

Step1: Calculate x - coordinate of P

The formula for the x - coordinate of the weighted average is $x_P=\frac{w_Ax_A + w_Bx_B}{w_A + w_B}$, where $w_A = 1$, $x_A=-5$, $w_B = 2$, and $x_B=-1$.
$x_P=\frac{1\times(-5)+2\times(-1)}{1 + 2}=\frac{-5-2}{3}=\frac{-7}{3}$

Step2: Calculate y - coordinate of P

The formula for the y - coordinate of the weighted average is $y_P=\frac{w_Ay_A + w_By_B}{w_A + w_B}$, where $w_A = 1$, $y_A = 6$, $w_B = 2$, and $y_B=-2$.
$y_P=\frac{1\times6+2\times(-2)}{1 + 2}=\frac{6 - 4}{3}=\frac{2}{3}$

Answer:

$P=(-\frac{7}{3},\frac{2}{3})$