Question

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

Answer 1

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.

Answer 2

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