Q. 20 - Calculus

Question

Explain why the location of the centroid relates only to the geometry of the region and not its mass.

Step-by-Step Solution

Answer

Centroid of the plane figure is defined as the point of intersection of the medians.

Step 1: Given information

The location of the centroid relates only to the geometry of the region and not it's mass.

Step 2: Calculation

For an example, take a triangle $A B C$ with vertices $(1,1),(2,0), and (2,3)$and join them. The point of intersection of medians $A D, B E$ and $C F$ is $G$