Final answer:
The length of the radius of the circle centered at (1, 3) passing through (4, 7) is calculated using the distance formula and is found to be 5 units.
Step-by-step explanation:
To find the length of the radius of the circle with the center at (1, 3) that passes through the point (4, 7), we need to use the distance formula between two points. The formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) is the center of the circle and (x2, y2) is a point on the circumference.
Substituting the given points into the formula:
Radius = √((4 - 1)² + (7 - 3)²)
Radius = √((3)² + (4)²)
Radius = √(9 + 16)
Radius = √25
Radius = 5 units