Final answer:
To determine the radius of the circle with center (2,2) and passing through (5,6), the distance formula is used, resulting in a radius of 5 units.
Step-by-step explanation:
The student has asked how to find the radius of a circle given its center and a point through which it passes. To determine the radius, we need to use the distance formula, which calculates the distance between two points in the plane. The distance formula is derived from the Pythagorean theorem and is stated as the square root of the sum of the squares of the differences in the x- and y-coordinates.
To find the radius of the circle with center at (2,2) and passing through (5,6), we use the distance formula:
- Subtract the x-coordinate of the center from the x-coordinate of the point on the circumference (5 - 2).
- Subtract the y-coordinate of the center from the y-coordinate of the point on the circumference (6 - 2).
- Square both of these differences (3^2 and 4^2).
- Add these squares together (9 + 16).
- Take the square root of this sum (√(25)), which gives us 5.
Therefore, the radius of the circle is 5 units.