Question

The centroid of the triangle with vertices \((1, -1)\), \((0, 6)\), and \((-3, 0)\) is:

• A. \(\left(\frac{2}{3}, \frac{5}{3}\right)\)
• B. \(\left(\frac{-2}{3}, \frac{-5}{3}\right)\)
• C. \(\left(\frac{-2}{3}, \frac{5}{3}\right)\)
• D. \(\left(\frac{2}{3}, \frac{-5}{3}\right)\)

Hint:

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

Answer 1

The Correct Option is A

The centroid \(G(x_G, y_G)\) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is given by the formula: \[ x_G = \frac{x_1 + x_2 + x_3}{3}, \quad y_G = \frac{y_1 + y_2 + y_3}{3} \] For the triangle with vertices \((1, -1)\), \((0, 6)\), and \((-3, 0)\), we have: \[ x_G = \frac{1 + 0 + (-3)}{3} = \frac{-2}{3}, \quad y_G = \frac{-1 + 6 + 0}{3} = \frac{5}{3} \] Thus, the centroid is \(\left(\frac{-2}{3}, \frac{5}{3}\right)\). Therefore, the correct answer is option (3).