Question

If \( A(-1,0) \), \( B(5,-2) \), and \( C(8,2) \) are the vertices of a triangle \( \triangle ABC \), then the coordinates of its centroid are:

• A. \( (12,0) \)
• B. \( (6,0) \)
• C. \( (0,6) \)
• D. \( (4,0) \)

Hint:

The centroid of a triangle is the average of the coordinates of its vertices: \[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

Answer 1

The Correct Option is D

The centroid formula states:
\[ G \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \] Substituting the given coordinates:
\[ G \left( \frac{-1 + 5 + 8}{3}, \frac{0 + (-2) + 2}{3} \right) = G \left( \frac{12}{3}, \frac{0}{3} \right) = (4,0) \]