Question

question 1-10
what are the coordinates of the centroid of △pqr with vertices p(-3, 5), q(1, 7), and r(2, 0)?
the centroid of △pqr is (

Explanation:

Step1: Recall centroid formula

The centroid \((\bar{x}, \bar{y})\) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), \((x_3, y_3)\) is given by \(\bar{x}=\frac{x_1 + x_2 + x_3}{3}\), \(\bar{y}=\frac{y_1 + y_2 + y_3}{3}\).

Step2: Identify coordinates

For \(\triangle PQR\), \(P(-3, 5)\), \(Q(1, 7)\), \(R(2, 0)\). So \(x_1=-3\), \(x_2 = 1\), \(x_3=2\); \(y_1 = 5\), \(y_2=7\), \(y_3 = 0\).

Step3: Calculate \(\bar{x}\)

\(\bar{x}=\frac{-3 + 1 + 2}{3}=\frac{0}{3}=0\).

Step4: Calculate \(\bar{y}\)

\(\bar{y}=\frac{5 + 7 + 0}{3}=\frac{12}{3}=4\).

Answer:

\((0, 4)\)