# Prove that the points (3, 0), (4, 5), (—1, 4) and (—2, —1), taken in order, form a rhombus. Also, find its area.

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Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.

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Let the given vertices be  A(3, 0), B(4, 5), c(-1, 4) and D(-2, -1)

Here all sides of the quadrilateral ABCD are off same lengths but the diagonals are of different lengths.

So, ABCD is a rhombus.

Therefore area of rhombus ABCD=(1/2)x4√2x6√2

=24 sq. units