Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.

Question

Philoid · Accepted Answer

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.