Question

find the centroid of triangle abc.
the centroid is located at the point ( , )

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of points \( A \), \( B \), and \( C \) from the graph.

• Point \( A \): \( (0, 3) \)
• Point \( B \): \( (2, 5) \)
• Point \( C \): \( (4, 1) \)

Step2: Use centroid formula

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

Substitute \( x_1 = 0 \), \( x_2 = 2 \), \( x_3 = 4 \); \( y_1 = 3 \), \( y_2 = 5 \), \( y_3 = 1 \):

\( G_x = \frac{0 + 2 + 4}{3} = \frac{6}{3} = 2 \)
\( G_y = \frac{3 + 5 + 1}{3} = \frac{9}{3} = 3 \)

Answer:

\( (2, 3) \)