centroid
point of concurrency of medians, 2/3 of distance from vertex to opposite side’s midpoint
The centroid is the geometric center of a shape. It is the point where all the medians intersect in a triangle. For any multi-sided polygon, the centroid is the point of balance where all the sides have equal weight.
In other words, the centroid is a point that lies at the intersection of all the straight lines that can be drawn from any point to the boundary of the shape. It is also known as the center of gravity or center of mass of the shape.
The centroid is an important concept in several fields such as physics, engineering, mathematics, and geometry. In engineering, it is used to determine the stability and balance of structures. In mathematics, it is used to find the center of a figure, which can be useful in calculating its area or volume.
The formula for finding the centroid of a two-dimensional shape such as a triangle, square, or rectangle is:
Centroid = [(x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3]
Where x1, x2, and x3 are the x-coordinates of the vertices of the shape, and y1, y2, and y3 are the y-coordinates of the vertices.
For a three-dimensional shape such as a sphere or cube, the formula for finding the centroid is more complex and involves integration.
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