Geometry

Question Analysis

The core goal is to figure out the coordinates of point A on a circle in the coordinate plane. We'll make use of the circle's center, its radius, and coordinate - system fundamentals to precisely pin down the location of A.

 

Key Concept Explanation

In the coordinate plane, points are expressed as . For a point on a circle, the distance from the circle's center  to that point is equal to the radius r. This relationship is described by the distance formula, which stems from the Pythagorean theorem: .

 

Step - by - Step Solution

Pinpoint the center and radius:

By looking at the graph, the center of the circle L has coordinates . Counting the grid units from the center L to a point on the circle reveals the radius .

The x - coordinate of point A is .

Utilize the distance formula:

Substitute , , , and  into