Geometry

Question Analysis

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

 

Key Concept Explanation

In the coordinate plane, a point is represented by an ordered pair . 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 between the center of the circle and any point on the circle 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. Determine the horizontal distance:

Point is on the - axis, so the horizontal distance from the center to point is units (from to ).

3. Use the Pythagorean theorem to find the vertical distance:

The radius of the circle is (by observing the grid). According to the Pythagorean theorem , where (horizontal distance) and is the vertical distance.

Substitute the values: , so

Click "Show Answer" to reveal the answer and analysis