Geometry

Question Analysis

The main focus is on determining the radius of a circle in the coordinate plane. The radius is the distance from the center of the circle to any point on its circumference, which can be calculated using the distance formula or by counting grid units.

 

Key Concept Explanation

The radius  of a circle is the length between the center  and a point  on the circle. Mathematically, . In a grid - based coordinate system, we can also visually count the number of grid units from the center to the edge of the circle.

 

Step - by - Step Solution

1. Locate the center of the circle:

By observing the graph, the center of the circle is at the point .

2. Find a point on the circumference:

Notice that the circle intersects the y - axis at  (for example).

3. Calculate the radius:

Using the distance formula with