Final answer:
The center of the circle with diameter endpoints (12,3) and (-8,5) is determined using the midpoint formula and is at the coordinates (2,4).
Step-by-step explanation:
To find the coordinates of the center of a circle given the endpoints of a diameter, you can simply find the midpoint between the two endpoints. The endpoints provided are (12,3) and (-8,5).
The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2).
Using the formula, we get the center of the circle to be ((12 - 8)/2, (3 + 5)/2), which simplifies to (2, 4). Therefore, the center of the circle is at the coordinates (2,4).