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Consider the right triangle shown in Figure 1. Along the hypotenuse, y = a x.
The area of the triangle is
The x coordinate of the centroid, X, multiplied by the area is equal to the integral of x multiplied by the area da. That is, it is the sum of the small areas da multiplied by their x coordinate.
where,
Therefore,
Solving for the x coordinate of the centroid, 
