Final answer:
To find the coordinates of the circle's center, use the midpoint formula with the endpoints of the diameter.
Step-by-step explanation:
To find the coordinates of the circle's center, we need to find the midpoint of the diameter.
The midpoint formula is ( (x1 + x2) / 2 , (y1 + y2) / 2 ). So, plugging in the values from the endpoints, we get: ( (4 + -2) / 2 , (-7 + -1) / 2 ).
Simplifying, we get the coordinates of the center as (1, -4).