The x-axis and y-axis are lines of symmetry for a square. if one of its vertices has coordinates ( a, b), then the vertice opposite it is

(-a, -b)

Step-by-step explanation:

It's a square that has both X-axis and Y-axis as lines of symmetry.  We can then conclude the center of the square is at the origin (0,0).

It doesn't matter if the square is straight up (both axis being the mid-points symmetry lines, and one corner in each quadrant) or if it is turned (both axis being the diagonals and the corners are on the axis), in any case if a summit (corner) is defined as (a,b), the opposite corner will be at (-a,-b).

(a,b) could be (2,2), then opposite would be (-2,-2).

(a,b) could be (3,0), then the opposite would be (-3,0).