Geometry

Question Analysis

The main focus is on determining the coordinates of point on the circle in the coordinate plane. We'll use the properties of the circle, such as the center and radius, along with the coordinate system to find the location of .

 

Key Concept Explanation

In the coordinate plane, a point is represented by . For a point on a circle, we can use the distance formula (derived from the Pythagorean theorem) based on the circle's center and radius . The distance from the center of the circle to any point on it (like ) is equal to the radius.

 

Step - by - Step Solution

1. Locate the center of the circle:

By observing the graph, the center of the circle has coordinates .

2. Estimate the radius:

By counting grid units from the center to a point on the circle (e.g., the right - most point), we find the radius .

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

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

Using the Pythagorean theorem

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