Answer :

In a Rhombus the sides are equal and the diagonals bisect each other at 90°

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by

.....(1)

Length AB = =

Length BC = =

Length CD = =

Length AD = =

Slope of a line between two points (a,b) and (c,d) is

Slope of Diagonal AC = = 1

Slope of diagonal BD = = -1

Note: If the Product of slopes of two lines = -1 then they are perpendicular to each other.

As the product of slopes pf two diagonals = -1. Hence they're perpendicular to each other.

Hence The given points form a rhombus.

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