Question

Derive the expression of centroid for a triangle

Answer 1

Answer:

The centroid of a triangle is located at the intersecting point of all three medians of a triangle. At the point of intersection (centroid), each median in a triangle is divided in the ratio of 2: 1.

Centroid of points, A, B and C is (x1+x2+x3)/3, (y1+y2+y3)/3. Centroid is a point where all the three medians of the triangle intersect. So,the centroid of triangle can be found by finding the average of the x-coordinate's value and the average of the y-coordinate's value of all the vertices of the triangle.

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Answer 2

Derive the expression for the centroid of right angled triangle. Along the hypotenuse, y = ax. 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.

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