Question

what is the average of the points a, b and c with weights 1, 3 and 4 respectively? (grid with points a, b, c plotted)

Explanation:

Step1: Find coordinates of A, B, C

From the graph: \( A(-7, 5) \), \( B(8, 2) \), \( C(5, 4) \)

Step2: Calculate weighted sum for x - coordinates

Weighted sum \( x=\frac{1\times(-7)+3\times8 + 4\times5}{1 + 3+4}=\frac{-7 + 24+20}{8}=\frac{37}{8}=4.625 \)

Step3: Calculate weighted sum for y - coordinates

Weighted sum \( y=\frac{1\times5+3\times2 + 4\times4}{1 + 3+4}=\frac{5 + 6+16}{8}=\frac{27}{8}=3.375 \)

Answer:

\((4.625, 3.375)\)