Geometry

Question Analysis

The main focus is to determine the centroid of the circle. For a circle, the centroid is its center, which is equidistant from all points on the circle. We rely on observing the circle's symmetry on the coordinate grid to find this central point.

Key Concept Explanation

The centroid of a circle is its geometric center. By definition, the radius is the fixed distance from the center to any point on the circle. In a coordinate system, we find the center by looking at how the circle is symmetrically arranged around a point with respect to the and axes.

Step - by - Step Solution

1. Visually inspect the circle:

Examine the circle's placement on the coordinate grid. Notice how it is symmetrically distributed around a specific point.

Through careful observation of the distances from the circle's edge to potential central points in both the and directions, we can see that the circle is centered at

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