Q. 245.0( 1 Vote )

# Show that the points A(1, 0), B(5, 3), C(2, 7) and D(- 2, 4) are the vertices of a rhombus.

Answer :

Given points are A(1, 0), B(5, 3), C(2, 7) and D(- 2, 4).

We need to prove that these are the vertices of a rhombus.

We know that in the lengths of sides are equal in a rhombus and the length of diagonals are not equal.

Let us find the lengths of the sides.

We know that the distance between the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is .

Now,

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⇒ AB = 5

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⇒

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⇒

⇒ BC = 5

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⇒

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⇒

⇒ CD = 5

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⇒

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⇒ DA = 5

We got AB = BC = CD = DA, these are the vertices of a square or a rhombus.

Now we find the lengths of the diagonals.

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We got AC = BD.

∴ The points form a square not rhombus.

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