Final answer:
The coordinates of the center of the circle are (8x - 3, 4y + 2), found by averaging the x-coordinates and y-coordinates of the endpoints of the diameter.
Step-by-step explanation:
The coordinates of the center of a circle can be found by averaging the x-coordinates and y-coordinates of the diameter's endpoints. Given the endpoints A(4x - 8, 6y + 7) and B(12x + 2, 2y - 3), we can find the center by calculating:
- Center's x-coordinate = (4x - 8 + 12x + 2) / 2 = (16x - 6) / 2 = 8x - 3.
- Center's y-coordinate = (6y + 7 + 2y - 3) / 2 = (8y + 4) / 2 = 4y + 2.
Therefore, the coordinates of the center of the circle in terms of x and y are (8x - 3, 4y + 2).