Question

The vertices of a triangle are \( (4, 6), (2, -2) \), and \( (0, 2) \). Then the coordinates of its centroid must be:

• A. \( (2, 3) \)
• B. \( (1, 2) \)
• C. \( (-2, 2) \)
• D. \( (2, 2) \)

Hint:

The centroid of a triangle is the point where the three medians intersect, and it can be found by averaging the coordinates of the three vertices.

Answer 1

The Correct Option is B

The centroid of a triangle is the average of the coordinates of its vertices. Given the vertices \( (4, 6), (2, -2), (0, 2) \), we can calculate the centroid as: \[ \text{Centroid} = \left( \frac{4 + 2 + 0}{3}, \frac{6 + (-2) + 2}{3} \right) \] \[ \text{Centroid} = \left( \frac{6}{3}, \frac{6}{3} \right) = (2, 2) \] Therefore, the correct answer is \( (1, 2) \).