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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