Final answer:
The question seeks to identify which endpoints could represent the diameter of a circle fitting into a square, with both measurements being equal. The perimeter of the circle would then be the circumference, 2πr, which should be less than the perimeter of the square but more than its diameter. Without further details, 2±√7 could be speculated to reference the endpoints of the diameter symmetrically placed around the center.
Step-by-step explanation:
The question seems to revolve around identifying which set of endpoints on a number line could represent the diameter of a circle when fitted inside a square, such that the diameter is equal to the side of the square (a=2r, where r is the radius of the circle and a is the side length of the square). The perimeter of the circle, being the circumference, is expressed as 2πr. Given that the circle fits inside the square, this perimeter must be less than the perimeter of the square, which is 4a, but significantly more than directly across the square, which is 2a.
To find the exact endpoints of the diameter using the mentions in the question, we can deduce that the endpoints must be distances from a center point that add up to the length of the diameter, which is twice the radius (2r). In this context, 2±√7 seems to provide a reasonable approximation, signifying endpoints that are symmetrically placed about the center (which could be 0). Without more context, it's difficult to conclusively state which option correctly represents the diameter endpoints as an actual number for the diameter or radius isn't provided.