Question

what is the average of the points a, b and c with weights 1, 4 and 4 respectively?

Explanation:

Step1: Find coordinates

Point \(A(0,4)\), \(B(2,-7)\), \(C(5,6)\)

Step2: Calculate x - average

\(x=\frac{1\times0 + 4\times2+4\times5}{1 + 4+4}=\frac{0 + 8+20}{9}=\frac{28}{9}\approx3.11\)

Step3: Calculate y - average

\(y=\frac{1\times4+4\times(-7)+4\times6}{1 + 4+4}=\frac{4-28 + 24}{9}=\frac{0}{9}=0\)

Answer:

\((\frac{28}{9},0)\)