Question

what are the coordinates of the centroid of δghi? simplify any fractions.

Explanation:

Step1: Identify coordinates of vertices

From the graph, we find the coordinates of \( G \), \( H \), and \( I \).

• \( G \): \( (5, 5) \)
• \( H \): \( (-3, -5) \)
• \( I \): \( (7, -3) \)

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:

$$ x = \frac{x_1 + x_2 + x_3}{3}, \quad y = \frac{y_1 + y_2 + y_3}{3} $$

Substitute \( x_1 = 5 \), \( x_2 = -3 \), \( x_3 = 7 \) for \( x \)-coordinate:

$$ x = \frac{5 + (-3) + 7}{3} = \frac{5 - 3 + 7}{3} = \frac{9}{3} = 3 $$

Substitute \( y_1 = 5 \), \( y_2 = -5 \), \( y_3 = -3 \) for \( y \)-coordinate:

$$ y = \frac{5 + (-5) + (-3)}{3} = \frac{5 - 5 - 3}{3} = \frac{-3}{3} = -1 $$

Answer:

\( (3, -1) \)