Midpoint and Centroid Formulas

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The midpoint of a segment is halfway between the endpoints and . The coordinates of are the averages of the coordinates of and .


For example, if and , then .

The point is the balancing point of and . More generally, the average of the coordinates of a finite set of points, designated , represents the balancing point, also called the centroid. To find the centroid of a curve or a region, you must use integral calculus!

The general formula for the midpoint of the points and is .

The general formula for the centroid of the points , , …, is .

You can select any number of black points between 2 and 100 with the centroid shown as a red point.


Contributed by: George Beck (August 2022)
Open content licensed under CC BY-NC-SA



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