what are the coordinates of the centroid of $\triangle abc$?\nsimplify any fractions.\n( , )
what are the coordinates of the centroid of $\triangle abc$?\nsimplify any fractions.\n( , )
Answer
Explanation:
Step1: Identify vertex coordinates
From the graph: $A(-5, 0)$, $B(1, -2)$, $C(1, 5)$
Step2: Apply centroid formula
The centroid $(G_x, G_y)$ of a triangle is the average of the vertices' coordinates: $$G_x = \frac{x_A + x_B + x_C}{3}, \quad G_y = \frac{y_A + y_B + y_C}{3}$$
Step3: Calculate x-coordinate
$$G_x = \frac{-5 + 1 + 1}{3} = \frac{-3}{3} = -1$$
Step4: Calculate y-coordinate
$$G_y = \frac{0 + (-2) + 5}{3} = \frac{3}{3} = 1$$
Answer:
$(-1, 1)$