Explanation

(b)
$|PQ| = \sqrt{(4 - 1)^{2} + (1 - 6)^{2}} = \sqrt{9 + 25} = \sqrt{34}$
$|QR| = \sqrt{(1 + 4)^{2} + (6 - 3)^{2}} = \sqrt{25 + 9} = \sqrt{34}$
$|RS| = \sqrt{( - 4 + 1)^{2} + (3 + 2)^{2}} = \sqrt{9 + 25} = \sqrt{34}$
$|SP| = \sqrt{( - 1 - 4)^{2} + ( - 2 - 1)^{2}} = \sqrt{25 + 9} = \sqrt{34}$
$\Rightarrow \ \ \ \ \ \ \ |PQ| = |QR| = |RS| = |SP|$
Now, $|PR| = \sqrt{( - 8)^{2} + (2)^{2}} = \sqrt{68}$
And, $|QS| = \sqrt{( - 2)^{2} + ( - 8)^{2}} = \sqrt{68}$
Hence, it is a square.