Each side of a square is of length 4.  The centre of the square is (3, 7) and one of its diagonals is parallel to y = x.  Then the coordinates of its vertices are

side of the square is 4, hypotenuse = 2s=42 half of 42 is 22slope of the diagonal parallel to y=x is 1, inclination=450 The point on the diagonal (vertices) on the line with inclination 450 and at a distance of 22 from centre(3,7)  using parametric form is x=x1±r cosθ,  y=y1±rsinθ  θ=π4x=3±22(12)           y=7±(22)(12) A(5,9)C(1,5)As diagonals are  perpendicular to slope of other diagonal is 1350θ=3π4The other two vertices areB(1,9)D(5,5)     ,