In triangle ABC, if the coordinates of the centroid are (3,4), and two vertices are (1,2) and (5,6), find the third vertex.
Show answer & explanation
Correct answer: A
Explanation
Centroid = (3, 4); Two vertices = (1, 2), (5, 6)
According to the formula:
Centroid = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
(1 + 5 + x)/3 = 3 ⇒ 6 + x = 9 ⇒ x = 3
(2 + 6 + y)/3 = 4 ⇒ 8 + y = 12 ⇒ y = 4
(3, 4)