In triangle ABC, the coordinates of vertices A and B are (0,0) and (6,0), respectively. Vertex C lies somewhere on the line 
, and the centroid of triangle ABC is (5,3). What are the coordinates of point C?
Show answer & explanation
Correct answer: D
Explanation
Centroid formula: ((x₁ + x₂ + x₃) ÷ 3, (y₁ + y₂ + y₃) ÷ 3)
C lies on y = x, so let C = (a, a).
⇒ (0 + 6 + a) ÷ 3 = 5
⇒ 6 + a = 15
⇒ a = 9
Therefore, C = (9, 9)