Question

Which ordered pairs would complete a square including the two points 3,4

Answer 1

There isn't enough information given to determine a specific square, since a square including the points (3,4) could have varying sizes and rotations.

For example, if you want a unit square with sides of length 1 that includes the point (3, 4), you could have a square with vertices (3, 4), (3, 5), (4, 4), (4, 5). Alternatively, you could have a square with vertices (3, 4), (2, 4), (2, 5), (3, 5).

To illustrate a rotated square, consider a square with sides of length √2 (about 1.41) and diagonals along the coordinate axes. In this case, you could have a square with vertices (3, 4), (2.59, 4.41), (3, 4.82), (3.41, 4.41).

There are infinitely many possible squares that could contain (3, 4), but these examples help to demonstrate the necessity of additional constraints or information.