Triangle Centroid
Triangle Centroid
\[\begin{aligned}
x &= \frac{x_1+x_2+x_3}{3} \\
y &= \frac{y_1+y_2+y_3}{3}
\end{aligned}\]
Variables
x = centroid x-coordinate
y = centroid y-coordinate
x1 = x-coordinate of vertex 1
y1 = y-coordinate of vertex 1
x2 = x-coordinate of vertex 2
y2 = y-coordinate of vertex 2
x3 = x-coordinate of vertex 3
y3 = y-coordinate of vertex 3
Description
What is this formula?
The triangle centroid formula calculates the coordinates of the centroid of a triangle. The centroid is the intersection point of the three medians and represents the geometric center of the triangle.
When to use it
Use this formula when the coordinates of the three triangle vertices are known and the center point of the triangle must be determined.
Example
For a triangle with vertices:
A(1,2)
B(5,2)
C(3,8)
The centroid coordinates are:
x = (1+5+3)/3 = 3
y = (2+2+8)/3 = 4
Therefore:
G = (3,4)
Applications
Used in geometry, physics, engineering, computer graphics, structural analysis, and finite element modeling.
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