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.

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 (x1, y1) and (x2, y2) is .

Now,

AB = 5

BC = 5

CD = 5

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.

We got AC = BD.

The points form a square not rhombus.

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