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Find square A(0,0),B(2,2),C(0,4),D(-2,2)

Solution:
Your problem `->` square A(0,0),B(2,2),C(0,4),D(-2,2)


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


`AB^2 = (2-0)^2 + (2-0)^2 = (2)^2 + (2)^2 = 4 + 4 = 8`

`BC^2 = (0-2)^2 + (4-2)^2 = (-2)^2 + (2)^2 = 4 + 4 = 8`

`CD^2 = (-2-0)^2 + (2-4)^2 = (-2)^2 + (-2)^2 = 4 + 4 = 8`

`AD^2 = (-2-0)^2 + (2-0)^2 = (-2)^2 + (2)^2 = 4 + 4 = 8`

`AC^2 = (0-0)^2 + (4-0)^2 = (0)^2 + (4)^2 = 0 + 16 = 16`

`BD^2 = (-2-2)^2 + (2-2)^2 = (-4)^2 + (0)^2 = 16 + 0 = 16`

Here ` AB^2=BC^2=CD^2=AD^2`

`:. AB=BC=CD=AD`

and ` AC^2=BD^2`

`:. AC=BD`

A quadrilateral, in which all sides are equal and also the diagonals are equal, is a square
`:.` ABCD is a square








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