If A(3,-4),B(4,5),C(5,-5),D(4,-10) are the vertices of a quadrilateral prove that ABCD is Rhombus?

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Solution

Let A(3,-4), B(4,5), C(5,-5) and D(4,-10) are the vertices of a quadrilateral ABCD.
To Proof : ABCD is a rhombus.
Proof :
Rhombus : All sides are equal and diagonals are at right angles and unequal.So,
Thus, all sides are equal. i.e., AB = BC = CD = DA
And,

Thus, diagonals are at right angles and unequal.
Hence, ABCD is a rhombus

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