AB =
\({\sqrt{{1+5)}^{2}+(3-5)^{2}+(0-2)^{2}}}\\=\sqrt{36+4+4}\\=\sqrt{44}\\=2\sqrt11
\)
BC =
\({\sqrt{{(-5+9)}^{2}+(5+1)^{2}+(2-2)^{2}}}\\=\sqrt{16+36+0}\\=\sqrt{52}\\=2\sqrt13
\)
CD =
\({\sqrt{{(-9+3)}^{2}+(-1+3)^{2}+(2-0)^{2}}}\\=\sqrt{36+4+4}\\=\sqrt{44}\\=2\sqrt11
\)
DA =
\({\sqrt{{(-3-1)}^{2}+(-3-3)^{2}+(0-0)^{2}}}\\=\sqrt{16+36+0}\\=\sqrt{42}\\=2\sqrt13
\)
Also, AC =
\({\sqrt{{(1+9)}^{2}+(3+1)^{2}+(0-2)^{2}}}\\=\sqrt{100+16+4}\\=\sqrt{120}\\=2\sqrt30
\)
Since AB =CD, BC = CA and AC ≠ BD
∴The opposite sides are equal and diagonals are unequal, so the given points are the vertices of a parallelogram not rectangle.