In a triangular steel frame, points A(0,0), B(6,0), and C(2,6) form a triangle. A vertical load acts at the centroid. What is the distance from vertex C to the centroid?
Show answer & explanation
Correct answer: B
Explanation
Given:
A(0,0), B(6,0), C(2,6)
According to the formula:
Centroid of the triangle
= ((x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3)
Centroid = ((0 + 6 + 2)/3 , (0 + 0 + 6)/3)
= (8/3 , 2)
Now, the distance from C(2,6) to the centroid
= √((2 − 8/3)² + (6 − 2)²)
= √((−2/3)² + 4²)
= √(4/9 + 16)
= √(148/9)
= √148 / 3
= √16.4 units