Find the coordinates of the center and the radius of the circle with

To find the coordinates of the center and the radius of the circle with diameter CD, you can follow these steps:

1. Find the midpoint of the line segment CD.
2. The midpoint of CD is also the center of the circle.
3. Calculate the distance between one of the endpoints (C or D) and the midpoint.
4. The distance between the midpoint and either endpoint is the radius of the circle.

Let's go through each step:

1. Finding the midpoint of the line segment CD:

To find the midpoint of a line segment, you can use the midpoint formula:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Given the coordinates of points C(-4, 2) and D(8, 8), we can use the midpoint formula to find the midpoint.

Midpoint = ((-4 + 8)/2, (2 + 8)/2)
= (4/2, 10/2)
= (2, 5)

Therefore, the midpoint of the line segment CD, and the center of the circle, is (2, 5).

2. Calculating the distance between one of the endpoints and the midpoint:

To calculate the distance between two points (x₁, y₁) and (x₂, y₂), you can use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distance between the endpoint D(8, 8) and the midpoint (2, 5).

Distance = √((2 - 8)² + (5 - 8)²)
= √((-6)² + (-3)²)
= √(36 + 9)
= √45

Therefore, the distance between the endpoint D and the midpoint is √45.

3. Radius of the circle:

Since the radius is the distance between the midpoint and either of the endpoints, the radius of the circle is equal to √45.

To summarize:
- The coordinates of the center of the circle are (2, 5).
- The radius of the circle is √45.