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Centroid of a triangle



The centroid of a triangle is the point where the three medians of a triangle meet or intersect An illustration of the centroid is shown below.


centroid-of-a-triangle-image


In the above graph, we call each line (in blue) a median of the triangle.

The median is the line that starts from a vertex and goes to the midpoint of the opposite side

After you construct all three medians, the point where they intersect ( shown in red ) is the centroid

Now, If you put a triangle on the coordinate system, you can easily get the centroid by doing some simple calculation


centroid-of-a-triangle-image


Call the centroid C, the formula to get the centroid is:

[( x1 + x2 + x3)/3, (y1 + y2 + y3)/3]

Example:

Find the centroid of the following triangle with veetices (1,2), (3,4), and (5,0)


centroid-of-a-triangle-image


C = [ (1 + 3 + 5) / 3 , (2 + 4 + 0) / 3 ] = (9/3 , 6/3) = (3,2)





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