Finding the radius of a circle on a graph can be done using various methods, depending on the information available. Here’s a step-by-step guide to help you determine the radius:
- Identify the Circle’s Center and a Point on the Circle: Look at the graph to find the center of the circle, which is often marked or can be determined from the equation of the circle. A point on the circle can be any point that lies on the circumference.
- Use the Distance Formula: Once you have the center of the circle (let’s call it (h, k)) and a point on the circle (let’s call it (x, y)), you can use the distance formula to find the radius. The formula for the distance (r) between two points is:
r = √((x – h)² + (y – k)²)
- Plug in the Coordinates: Substitute the coordinates of the center and the point into the formula. For example, if the center is (3, 2) and the point on the circle is (5, 5), you would have:
r = √((5 – 3)² + (5 – 2)²)
- Simplify the Equation: Perform the calculations:
r = √(2² + 3²) = √(4 + 9) = √13
- Calculate the Radius: The final answer gives you the radius of the circle. In this example, the radius is √13 units.
By following these steps, you should be able to determine the radius of any circle plotted on a graph, provided you have the center and a point on the circumference.