Geometry

Question Analysis

The primary objective is to determine the coordinates of point situated on a circle within the coordinate plane. By leveraging the circle's center, radius, and the principles of the coordinate system, we can precisely establish the location of .

 

Key Concept Explanation

In the coordinate plane, points are denoted as . For any point on a circle, the distance from the circle's center to that point is equivalent to the radius . This relationship is encapsulated by the distance formula, which is derived from the Pythagorean theorem: .

 

Step - by - Step Solution

1. Identify the center of the circle:

Through observation of the graph, the center of the circle is found to have coordinates .

2. Ascertain the radius:

By counting the grid units from the center to a point on the circle,  the radius is determined.

3. Determine the position of point relative to the center:

The - coordinate of is . The horizontal distance from the center to is calculated as