Question

what is the locus of points that are equidistant from the four vertices of a square?

Answer 1

Intersection of the diagonals?

Answer 2

There is only one point that is equidistant from all four vertices and that is the intersection of the diagonals of the square.

Answer 3

Center the square at the origin. If you are in the upper half of the plane, then you are closer to one of the upper points than one of the lower points, aren't you? Same idea for the lower half of the plane, and the left half of the plane, and the right half of the plane.

So that leaves only one point as a possible candidate...

Answer 4

thank you!