If the diameter of a circle has endpoints A(7, 2) and B(1, 8), where is the center of the circle?

To find the center of the circle formed by the diameter with endpoints A(7, 2) and B(1, 8), we need to calculate the midpoint of the line segment connecting these two points.

The formula for finding the midpoint, M, of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is:

M = (x₁ + x₂) / 2, (y₁ + y₂) / 2

Here, our points are:

A(7, 2): (x₁, y₁) = (7, 2)

B(1, 8): (x₂, y₂) = (1, 8)

Substituting these values into the midpoint formula gives us:

M = ((7 + 1) / 2, (2 + 8) / 2)

Calculating each component:

M = (8 / 2, 10 / 2)

M = (4, 5)

Therefore, the center of the circle is located at the point (4, 5).