Final answer:
The radius of the circle with endpoints (-4, 3) and (2, -1) is found using the distance formula to calculate the diameter and then dividing it by 2. The closest whole number to the radius is 5, making the correct answer (d) 5.
Step-by-step explanation:
The student is asking about the radius of a circle with a given pair of endpoints of a diameter. First, we find the length of the diameter by using the distance formula between the two points (-4, 3) and (2, -1). The formula is √((x2 - x1)² + (y2 - y1)²), which results in the diameter of the circle. We compute this as √((2 - (-4))² + ((-1) - 3)²) = √(6² + (-4)²) = √(36 + 16) = √52.
The diameter of the circle is therefore √52 units. Since the diameter is equal to twice the radius (D = 2r), we divide the diameter by 2 to find the radius: radius = (√52) / 2. This simplifies to √13, which is approximately 3.61. However, in this context, we are looking for the closest whole number which matches one of the provided options, hence the correct answer is (d) 5, since √13 is closest to 5.