Finding the Centroid of a Triangle | Formula, Calculation, and Example

Centroid (defn)

The centroid of a two-dimensional shape, such as a triangle or a polygon, is the point where all the medians of the shape intersect

The centroid of a two-dimensional shape, such as a triangle or a polygon, is the point where all the medians of the shape intersect. In other words, the centroid is the balance point of the shape. It can be thought of as the geometric center or the average position of all the points in the shape.

To find the centroid of a triangle, you can use the following formula:

Centroid = ( (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3 )

Here, (x1, y1), (x2, y2), and (x3, y3) represent the coordinates of the triangle’s vertices. By calculating the average of the x-coordinates and y-coordinates separately, you can find the coordinates of the centroid.

For example, let’s say we have a triangle with vertices at (1, 2), (4, 6), and (7, 3). To find the centroid, we can use the formula:

Centroid = ( (1 + 4 + 7) / 3, (2 + 6 + 3) / 3 )

Simplifying this expression, we get:

Centroid = (4, 11/3)

So, the centroid of the given triangle is (4, 11/3), which represents the balance point of the triangle.

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