# Show that following points are vertices of a square: (0,1) , (1,4) , (4,3) , (3,0).

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let these points form a quadrilateral ABCD
here A ( 0,1)    B (1,4)    C ( 4,3)   D ( 3,0)

properties of a square =  all sides are equal and all diagnols are equal

length of side ab = root 10 ( by applying distance formula)
length of side bc = root 10 ( by applying distance formula)
length of side cd = root 10 ( by applying distance formula)
length of side ad = root 10 ( by applying distance formula )

length of diagonal ac = root 20 ( by applying distance formula )
length of diagonal bd = root 20 ( by applying distance formula )

as all the sides and both the diagonals of the quadrilateral are equal , hence it is a square
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