Understanding the Centroid | Definition, Calculation, and Applications in Geometry, Physics, and Engineering

Centroid

The centroid is a point that describes the balance or center of mass of a geometric shape

The centroid is a point that describes the balance or center of mass of a geometric shape. It is commonly used in geometry, particularly in dealing with polygons and three-dimensional shapes.

For a two-dimensional figure, such as a triangle or a polygon, the centroid is the point where all the medians intersect. A median is a line segment that connects one vertex of the figure to the midpoint of the opposite side. The centroid is the average of the coordinates of all the vertices of the figure.

In a triangle, the centroid is often denoted by the point G. To find the coordinates of the centroid of a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), you can use the following formulas:

x coordinate of the centroid (Gx) = (x₁ + x₂ + x₃) / 3
y coordinate of the centroid (Gy) = (y₁ + y₂ + y₃) / 3

For example, if the vertices of a triangle are A(2, 4), B(6, 8), and C(10, 2), the centroid (G) would have coordinates:

Gx = (2 + 6 + 10) / 3 = 6
Gy = (4 + 8 + 2) / 3 = 4

So the centroid of this triangle would be located at (6, 4).

The centroid is an important concept in various areas of mathematics, physics, and engineering. It plays a role in determining the balance and stability of objects, calculating centers of gravity, and analyzing shapes and their properties.

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