Show that A(-3, 2), B (-5, -5), C (2, -3) and D(4, 4) are the vertices of a rhombus.

Given points are A(-3, 2), B (-5, -5), C (2, -3) and D(4, 4)



By distance formula,


XY =


For AB ,


AB =


=


= units


For BC ,


BC =


=


= units


For CD,


CD =


=


= units


For AD ,


AB =


=


= units


Here we can observe that all lengths of □PQRS are equal.


Now for diagonal AC,


AC =


=


= units


Now for diagonal BD,


BD =


=


= units


Here in □ABCD, diagonals are unequal.


We know that a quadrilateral whose all sides are equal and diagonals are unequal, it is a rhombus.


Hence, our □ABCD is rhombus .


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