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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