The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Here given points are A (2, 0), B (9, 1), C (11, 6) and D (4, 4).
For a quadrilateral to be rhombus, all sides must be equal.
By distance formula,
XY =
For side AB,
AB =
=
= units.
For BC,
BC =
=
= units
CD =
=
= units.
AD =
=
= units.
Here all sides are unequal.
Hence □ABCD is not a rhombus.