Question

what are the coordinates of the centroid of δabc? simplify any fractions. ( , )

Explanation:

Step1: Find coordinates of A, B, C

From the graph, \( A(-6, 5) \), \( B(4, 3) \), \( C(-4, -5) \).

Step2: Use 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 \( x=\frac{x_1 + x_2 + x_3}{3} \), \( y=\frac{y_1 + y_2 + y_3}{3} \).

For \( x \)-coordinate:
\( x=\frac{-6 + 4 + (-4)}{3}=\frac{-6 + 4 - 4}{3}=\frac{-6}{3}=-2 \)

For \( y \)-coordinate:
\( y=\frac{5 + 3 + (-5)}{3}=\frac{5 + 3 - 5}{3}=\frac{3}{3}=1 \)

Answer:

\((-2, 1)\)