Question

what are the coordinates of the centroid of a triangle with vertices d(0, 1), e(2, 6), and f(7, 2)? enter your answer by filling in the boxes (\boxed{}, \boxed{})

Explanation:

Step1: Recall centroid formula

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

Step2: Calculate x - coordinate

For vertices \( D(0, 1) \), \( E(2, 6) \), \( F(7, 2) \), \( x_1 = 0 \), \( x_2 = 2 \), \( x_3 = 7 \).
\( x=\frac{0 + 2 + 7}{3}=\frac{9}{3}=3 \).

Step3: Calculate y - coordinate

\( y_1 = 1 \), \( y_2 = 6 \), \( y_3 = 2 \).
\( y=\frac{1 + 6 + 2}{3}=\frac{9}{3}=3 \).

Answer:

\( (3, 3) \)