Question

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

Answer 1

please refer the attachment.
Hope this helps you quickly

Answer 2

Answer:

The length of all sides are same and the length of both the diagonals are same, therefore the given figure is a square.

Step-by-step explanation:

The vertices of polygon are A(4,3) , B(6,4) , C(5,6) and D(3,5).

The distance formula is

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$AB=\sqrt{(4-6)^2+(3-4)^2}=\sqrt{5}$

$BC=\sqrt{(6-5)^2+(4-6)^2}=\sqrt{5}$

$CD=\sqrt{(5-3)^2+(6-5)^2}=\sqrt{5}$

$AD=\sqrt{(4-3)^2+(3-5)^2}=\sqrt{5}$

The length of all sides are same.

The length of diagonals are

$AC=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{10}$

$BD=\sqrt{(6-3)^2+(4-5)^2}=\sqrt{10}$

The length of both the diagonals are same.

Since the length of all sides are same and the length of both the diagonals are same, therefore the given figure is a square.