Question

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

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

Hint:

To find the centroid of a triangle, average the x-coordinates and y-coordinates of the vertices.

Answer 1

The Correct Option is D

Step 1: The centroid of a triangle is the average of the coordinates of the three vertices. The formula for the centroid is: \[ \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \] Step 2: Using the given vertices \( A(-1, 0), B(5, -2), C(8, 2) \): \[ \left( \frac{-1 + 5 + 8}{3}, \frac{0 + (-2) + 2}{3} \right) = \left( \frac{12}{3}, \frac{0}{3} \right) = (4, 0) \] Thus, the correct answer is \( (4, 0) \).