Question

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

Explanation:

Step1: Find coordinates of points

From the graph, \(A=(8,3)\), \(B = (-6,-5)\), \(C=(7,-6)\)

Step2: Calculate weighted average formula

The weighted average formula for coordinates \((x,y)\) is \(\bar{x}=\frac{w_1x_1 + w_2x_2+w_3x_3}{w_1 + w_2+w_3}\), \(\bar{y}=\frac{w_1y_1 + w_2y_2+w_3y_3}{w_1 + w_2+w_3}\) where \(w_1 = 1\), \(w_2=2\), \(w_3 = 2\)

For \(x -\) coordinate:

\(\bar{x}=\frac{1\times8+2\times(-6)+2\times7}{1 + 2+2}=\frac{8-12 + 14}{5}=\frac{10}{5}=2\)

For \(y -\) coordinate:

\(\bar{y}=\frac{1\times3+2\times(-5)+2\times(-6)}{1 + 2+2}=\frac{3-10-12}{5}=\frac{-19}{5}=-3.8\)

Answer:

\((2,-3.8)\)