Final answer:
The student's mathematics question involves finding the radius of a circle given its center and a point on the circle. The radius is determined to be √2 using the distance formula applied to coordinates (13,2) for the center and (12,1) for a point on the circle.
Step-by-step explanation:
The student's question pertains to the coordinate system of a circle in mathematics. Given the center of the circle at (13,2) and a point on the circle at (12,1), we can find the radius of the circle using the distance formula. The formula for the distance between two points (x1, y1) and (x2, y2) in a coordinate system is √((x2 - x1)² + (y2 - y1)²).
To find the radius:
- Calculate the difference between the x-coordinates: 13 - 12 = 1.
- Calculate the difference between the y-coordinates: 2 - 1 = 1.
- Apply the differences to the distance formula: radius = √((1)² + (1)²) = √(1 + 1) = √2.
The radius of the circle is √2. From this information, you could describe the circle equation or convert other points using the new origin at the center (13,2), which effectively shifts the coordinate system.