Geometry

Question Analysis

The main focus of this problem is to accurately determine the coordinates of the center of a circle plotted on the coordinate plane.

Key Concept Explanation

In the coordinate plane, the center of a circle is represented by an ordered pair . The  - coordinate indicates the horizontal position relative to the origin (negative values are to the left, positive values are to the right), and the  - coordinate indicates the vertical position (negative values are below the origin, positive values are above).

Step - by - Step Solution

1. Determine the x - coordinate:

Observe the horizontal position of the circle's center. By counting the grid lines along the x - axis, we can see that the center is 2 units to the left of the origin. So, the  - coordinate is .

2. Determine the y - coordinate:

Look at the vertical position of the circle's center. Counting the grid lines along the y - axis, the center is 1 unit below the origin. Thus, the  - coordinate is .

3. Form the coordinate pair:

Combining these values, the coordinates of the center of the circle are

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