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Find rhombus A(3,0),B(4,5),C(-1,4),D(-2,-1)

Solution:
Your problem `->` rhombus A(3,0),B(4,5),C(-1,4),D(-2,-1)


Here `A(3,0), B(4,5), C(-1,4), D(-2,-1)` are the given points


`AB^2 = (4-3)^2 + (5-0)^2 = (1)^2 + (5)^2 = 1 + 25 = 26`

`BC^2 = (-1-4)^2 + (4-5)^2 = (-5)^2 + (-1)^2 = 25 + 1 = 26`

`CD^2 = (-2+1)^2 + (-1-4)^2 = (-1)^2 + (-5)^2 = 1 + 25 = 26`

`AD^2 = (-2-3)^2 + (-1-0)^2 = (-5)^2 + (-1)^2 = 25 + 1 = 26`

`:. AB^2=BC^2=CD^2=AD^2`

`:. AB=BC=CD=AD`

A quadrilateral, in which all sides are equal, is a rhombus
`:.` ABCD is a rhombus








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