If the centroid of a triangle is at the origin (0,0) and two of its vertices are at (3,5) and (-4,1), what are the coordinates of the third vertex?
Show answer & explanation
Correct answer: A
Explanation
Given:
Centroid of triangle = (0, 0)
First vertex = (3, 5)
Second vertex = (-4, 1)
Third vertex = (x, y)
By formula:
Centroid = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
(3 + (−4) + x)/3 = 0
(−1 + x)/3 = 0
−1 + x = 0
x = 1
(5 + 1 + y)/3 = 0
(6 + y)/3 = 0
6 + y = 0
y = −6
Coordinates of third vertex = (1, −6)