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 .