Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.
Let given points be A(4, 3), B(6, 4), C(5, 6) and D(3, 5).
By distance formula,
XY =
For AB,
AB =
=
= units.
For BC,
BC =
=
= units.
For CD,
CD =
=
= units.
For AD,
AD =
=
= units.
Here, we can observe that □ABCD is a parallelogram.
Now,
For diagonal AC,
AC =
=
= units.
For diagonal BD,
BD =
=
= units.
∴ AC = BD, which means diagonals are equal.
We know that quadrilateral in which all sides are equal and diagonals are equal, is a square.
∴□ABCD is a square.