ABC is a triangle with A(3, 5). The mid-points of sides AB, AC are at (–1, 2), (6, 4) respectively. What are the coordinates of centroid of the triangle ABC?

Midpoint of AB = (–1, 2) gives B = (2(–1) – 3, 2(2) – 5) = (–5, –1). Midpoint of AC = (6, 4) gives C = (2(6) – 3, 2(4) – 5) = (9, 3). Centroid = ((3 + (–5) + 9)/3, (5 + (–1) + 3)/3) = (7/3, 7/3). Hmm that gives option (b). Let me recheck: A(3,5), B(–5,–1), C(9,3). Sum x: 3 – 5 + 9 = 7, so x_c = 7/3. Sum y: 5 – 1 + 3 = 7, so y_c = 7/3. The centroid is (7/3, 7/3), option (b).