If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
- A. (-1, 7/3)
- B. (-1/3, 7/3)
- C. (1, 7/3)
- D. (1/3, 7/3)
Answer: C. (1, 7/3)
Explanation: Let vertex A = (1, 1). Midpoint of AB = (-1, 2) ⇒ B = (2(-1)−1, 2(2)−1) = (-3, 3). Midpoint of AC = (3, 2) ⇒ C = (2(3)−1, 2(2)−1) = (5, 3). Centroid G = ((1 − 3 + 5)/3, (1 + 3 + 3)/3) = (3/3, 7/3) = (1, 7/3).