Geometry

Question Analysis

The main focus is to find the centroid of the circle. For a circle, the centroid is its geometric center, which is equidistant from all points on the circle.

 

Key Concept Explanation

The centroid of a circle is the center point of the circle. By definition, every point on the circle lies at a fixed distance (the radius) from this center. In a coordinate system, we can determine the coordinates of the center based on the circle's position.

 

Step - by - Step Solution

1. Observe the position of the circle on the coordinate grid.

Notice that the circle is symmetrically placed around the point .

Since the circle's centroid is its center, and by visually inspecting the symmetry of the circle with respect to the and axes on the grid, we can directly identify the coordinates of the center.

 

Common Mistakes

Misinterpreting the circle's position: Incorrectly identifying the center of the circle due to visual misjudgment or not properly observing the symmetry.

Confusing with other shapes' centroid concepts: Applying the centroid formul...