Let A(-1,-2) B(1,0) C(-1,2) D(-3,0) be the given points.Distance formula
=√((x2 - x1)2 + (y2 - y1)2)
AB=√((+)2 + (+)2)
=√
=√2
BC=√((--)2 + (-)2)
=√
=√2
CD=√((-+)2 + (-)2)
=√
=√2
AD=√((-+)2 + (+)2)
=√
=√2
AC=√((-+)2 + (+)2)
=√
=units
BD=√((--)2 + (-)2)
=√
=units
In ABCD AB=BC=CD=AD - four sides are equal.
AC=BD diagonals are equal.
Hence the given points form a square.