Question

Given the endpoints of a diameter of a circle, A(-1,1) and B(0.5,-3), find the coordinates of the center and the radius of the circle. Correct the answers to three decimal places.

A) Center: (-0.250, -1.000), Radius: 2.828
B) Center: (0.250, -1.000), Radius: 2.828
C) Center: (-0.250, -1.000), Radius: 3.536
D) Center: (0.250, -1.000), Radius: 3.536

Answer 1

To find the coordinates of the center and the radius of the circle, we can use the midpoint formula to find the center and the distance formula to find the radius.

The midpoint formula is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using the coordinates of A(-1,1) and B(0.5,-3), we can calculate the midpoint:
Midpoint = ((-1 + 0.5) / 2, (1 + -3) / 2)
Midpoint = (-0.25, -1)

The distance formula is:
Distance = √((x2 - x1)² + (y2 - y1)²)

Using the coordinates of A(-1,1) and B(0.5,-3), we can calculate the distance:
Distance = √((0.5 - (-1))² + (-3 - 1)²)
Distance = √((1.5)² + (-4)²)
Distance = √(2.25 + 16)
Distance = √18.25
Distance ≈ 4.272

Therefore, the correct answer is:
Center: (-0.250, -1.000)
Radius: 4.272

The correct answer is not provided in the options given.

Answer 2

To find the coordinates of the center and the radius of the circle, find the midpoint between the two given endpoints and calculate the distance between one of the endpoints and the center using the distance formula.

Step-by-step explanation:

To find the coordinates of the center and the radius of the circle, we need to first find the midpoint between the two given endpoints. The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, the coordinates of the center are (-0.250, -1.000).

To find the radius, we need to find the distance between one of the endpoints and the center of the circle. We can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the formula with the coordinates of one of the endpoints (-1, 1) and the center (-0.250, -1.000), we find the distance to be approximately 2.828.

Therefore, the correct answer is option A) Center: (-0.250, -1.000), Radius: 2.828.