Question

given two points which represent the endpoints of the diameter of a circle, which of the following statements is true? choose the correct statement. a. the x - coordinate of the center of the circle must be the same as at least one of the x - coordinates of the given endpoints of the diameter. b. the y - coordinate of the center of the circle must be the same as at least one of the y - coordinates of the given endpoints of the diameter. c. the center of the circle is the midpoint of the given endpoints of the diameter. d. the center of the circle cannot be found without additional information.

Explanation:

The center of a circle is the mid - point of its diameter. The x - coordinate and y - coordinate of the center are the averages of the x - coordinates and y - coordinates of the endpoints of the diameter respectively, and not necessarily equal to any of the coordinates of the endpoints. So, given the endpoints of the diameter, the center can be found as the mid - point.

Answer:

C. The center of the circle is the midpoint of the given endpoints of the diameter