Final answer:
The coordinates of the other end of the diameter of the circle, given one endpoint (4, -1) and the center (1, -3), are (-2, -5). This is obtained by solving the midpoint formula equations.
Step-by-step explanation:
In order to find the coordinates of the other end of the diameter of the circle, we need to use the concept of midpoint. In this case, the midpoint of the line connecting the two endpoints of the diameter is the center of the circle. Therefore, we use the midpoint formula to find the coordinates of the other end.
The midpoint formula is: (x1+x2)/2 = x, (y1+y2)/2 = y. Given the coordinates of one end (x1, y1) = (4, -1) and the center (x, y) = (1, -3), we can substitute in and solve the equation to get the coordinates (x2, y2) of the other end.
For the x-coordinate, we have: (4+x2)/2 = 1, theirfore x2 = 2*1 - 4 = -2. For the y-coordinate, we have: (-1+y2)/2 = -3, therefore y2 = 2*(-3) - (-1) = -5.
So, the coordinates of the other end of the diameter are (-2, -5).
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