Question

what are the coordinates of the centroid of \\( \triangle pqr \\)?
simplify any fractions.

Explanation:

Step1: Find coordinates of \(P\), \(Q\), \(R\)

From the graph, \(P(-7,6)\), \(Q(4,1)\), \(R(4,8)\)

Step2: Use centroid formula \((\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})\)

Here \(x_1=-7\), \(x_2 = 4\), \(x_3=4\); \(y_1 = 6\), \(y_2=1\), \(y_3 = 8\)
For \(x\)-coordinate: \(\frac{-7+4 + 4}{3}=\frac{1}{3}\)
For \(y\)-coordinate: \(\frac{6 + 1+8}{3}=5\)

Answer:

\((\frac{1}{3},5)\)