The polar coordinates of the two opposite bordering points of a diagonal of a square are (6,3) & (-2,-3). What are the coordinates of the other two bordering points?

those are strange polar coordinates, but what the heck. In rectangular form, they are

(-5.940,0.847) and (1.980,0.282)
The midpoint of that segment is (-1.980,0.564)
The slope of the segment is -0.071
So, since the diagonals are perpendicular, the other diagonal has slope 14.018

Now just find the end points of a segment as long as the first diagonal, such that the segment goes through the midpoint with the required slope.