Question

Show that the points P(0,-2) Q(3,1) R(0,4) S(-3,1) are the vertices of a square. PQRS

Answer 1

PR²= (0-0)²+(-2-4)²= 36
SQ²=(-3-3)²+(1-1)²= 36
the above two diagonals are equal further, PQ²= 18
QR²= 18
so the proof is obvious

Answer 2

Use the formula
$\sqrt{(x2 - x1) {}^{2} } - (y2 - y1) {}^{2}$
for PQ, QR, RS, SP and all the values will be equal to
$\sqrt{18} units$
Hence the given points are vertices of a square