Question

Centroid of a polygon is

• A. geometric center of the polygon.
• B. arithmetic mean position of all its vertices in two coordinate directions.
• C. the point at which a cutout of the polygon could be perfectly balanced on the tip of a pin.
• D. center of polyline.

Hint:

The centroid is the point at which a shape can be perfectly balanced. For polygons, it can be calculated as the average of the coordinates of its vertices, and it is the geometric center of the polygon.

Answer 1

The Correct Option is A, B, C

The centroid of a polygon is a key concept in geometry, often referred to as the "center of mass" or "center of gravity" of a shape. It is the point at which a cutout of the polygon could be perfectly balanced on the tip of a pin. The centroid is also the arithmetic mean position of all the vertices of the polygon, considered in both coordinate directions (x and y). In other words, the centroid is the geometric center of the polygon. Step 1: Explanation of the options
- Option (A): The centroid is indeed the geometric center of the polygon. This means that if the shape of the polygon were made of a uniform material, the centroid would be the point where the material could balance perfectly.
- Option (B): The centroid can also be described as the arithmetic mean position of all the vertices in both coordinate directions. This is a mathematical representation of the centroid, where we calculate the average of the x-coordinates and the y-coordinates of the polygon's vertices.
- Option (C): This is another correct description of the centroid. It is the point at which a cutout of the polygon could be balanced perfectly, which directly aligns with the definition of the centroid in physical terms.
- Option (D): The center of the polyline is not the same as the centroid. A polyline is a series of connected line segments, and its center does not necessarily correspond to the centroid of the enclosed area, so this option is incorrect. Thus, the correct answers are (A), (B), and (C).