Q. 123.6( 9 Votes )
Show that A(3, 2), B(0, 5), C(-3, 2) and D(0, -1) are the vertices of a square.
Answer :
Given: The points are A(3, 2), B(0, 5), C(-3, 2) and D(0, -1).
Note: For a quadrilateral to be a square, all the sides of the quadrilateral must be equal in length and the diagonals must be equal in length as well.
AB 
= 3√2 units
BC 
= 3√2 units
CD 
= 3√2 units
DA 
= 3√2 units
Therefore, AB = BC = CD = DA …..(1)
AC 
= 6 units
BD 
= 6 units
Therefore, AC = BD …..(2)
From 1 and 2, we have all the sides of ABCD are equal and the diagonals are equal in length as well.
Therefore, ABCD is a square.
Hence, the points A, B, C and D are the vertices of a square.
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