Final answer:
The y-coordinate of the other end of the diameter of the circle is -11. This is found by applying the midpoint formula to the given coordinates, confirming that option b is correct.
Step-by-step explanation:
The given problem is a coordinate geometry question that asks us to find the y-coordinate of the other end of a diameter of a circle, where we are given one end of the diameter, and the center of the circle. The coordinates given for one end of the diameter are (2,3) and the center of the circle is at (-2,5). If (-6,y) is the other end of the diameter, we find y using the fact that the center of the circle is the midpoint of the diameter. The midpoint formula is M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint, and (x1, y1), (x2, y2) are the endpoints of the diameter.
Substituting the known values into the midpoint formula, we get:
(-2,5) = ((2 + (-6))/2, (3 + y)/2)
By solving these equations, we find that the y-coordinate of the other end of the diameter is -11, which corresponds to option b.