Question

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

Explanation:

Step1: Identify coordinates

Assume \(A=(0, - 8)\), \(B=(0,2)\), \(C=(0,8)\) (reading from the graph).

Step2: Calculate average of y - coordinates

The formula for weighted - average of \(y\) - coordinates \(y_{avg}=\frac{w_1y_1 + w_2y_2+w_3y_3}{w_1 + w_2+w_3}\), where \(w_1 = 1\), \(w_2 = 1\), \(w_3 = 1\), \(y_1=-8\), \(y_2 = 2\), \(y_3 = 8\).
\[y_{avg}=\frac{1\times(-8)+1\times2 + 1\times8}{1 + 1+1}=\frac{-8 + 2+8}{3}=\frac{2}{3}\]
Since the \(x\) - coordinates of all points are \(0\), the average point is \((0,\frac{2}{3})\)

Answer:

\((0,\frac{2}{3})\)