Question

what is the average of the points a, b and c with weights 3, 1 and 2 respectively?

Explanation:

Step1: Identify the y - coordinates of points

Let the y - coordinate of point A be $y_A=-8$, point B be $y_B = - 9$, and point C be $y_C=6$.

Step2: Calculate the weighted - sum

The formula for the weighted average $\bar{y}=\frac{w_1y_1 + w_2y_2+w_3y_3}{w_1 + w_2+w_3}$, where $w_1 = 3$, $w_2 = 1$, $w_3 = 2$, $y_1=-8$, $y_2=-9$, $y_3 = 6$.
First, calculate the numerator: $w_1y_1+w_2y_2 + w_3y_3=3\times(-8)+1\times(-9)+2\times6=-24 - 9+12=-21$.
Then, calculate the denominator: $w_1 + w_2+w_3=3 + 1+2=6$.

Step3: Calculate the weighted average

$\bar{y}=\frac{-21}{6}=-\frac{7}{2}=-3.5$

Answer:

$-3.5$