What is the center of a circle if its diameter endpoints are (2, 8) and (6, 4)?

To find the center of a circle given the endpoints of its diameter, we need to calculate the midpoint between these two points. The formula for the midpoint

M = (x₁ + x₂, y₁ + y₂) / 2

In this case, the endpoints of the diameter are:

• Point 1 (x₁, y₁): (2, 8)
• Point 2 (x₂, y₂): (6, 4)

Now, substitute the coordinates into the midpoint formula:

• M = ((2 + 6) / 2, (8 + 4) / 2)
• M = (8 / 2, 12 / 2)
• M = (4, 6)

Therefore, the center of the circle is located at the coordinates (4, 6).