Geometry

Question Analysis

The main focus is to determine the centroid of the circle. For a circle, the centroid is its center, which is the point equidistant from all points on the circle. We need to accurately identify this central point based on the circle's position on the coordinate grid.

Key Concept Explanation

The centroid of a circle is its geometric center. By definition, the distance from the center to any point on the circle (the radius) is constant. In a coordinate system, we find the center by observing the circle's symmetry about the and axes.

Step - by - Step Solution

1. Visually inspect the circle:

Look at how the circle is positioned on the grid. Notice the symmetry of the circle around a particular point.

By carefully examining the distances from the circle's edge to potential central points in both the and directions, we can determine that the circle is centered at

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