Q. 144.2( 9 Votes )

Show that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus.

Answer :


Given: Vertices of the quadrilateral are A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2).


Note: For a quadrilateral to be a rhombus, all the sides must be equal in length and the diagonals must not be equal.


AB


= √26 units


BC


= √26 units


CD


= √26 units


DA


= √26 units


Therefore, AB = BC = CD = DA …..(1)


AC


= 4√2 units


BD


= 6√2 units


Also, AC BD …..(2)


From 1 and 2, we have all the sides are equal and diagonals are not equal.


Hence, the points A, B, C and D are the vertices of a rhombus.


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