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Find rectangle A(1,-1),B(-2,2),C(4,8),D(7,5)

Solution:
Your problem `->` rectangle A(1,-1),B(-2,2),C(4,8),D(7,5)


Here `A(1,-1), B(-2,2), C(4,8), D(7,5)` are the given points


`AB^2 = (-2-1)^2 + (2+1)^2 = (-3)^2 + (3)^2 = 9 + 9 = 18`

`CD^2 = (7-4)^2 + (5-8)^2 = (3)^2 + (-3)^2 = 9 + 9 = 18`

`BC^2 = (4+2)^2 + (8-2)^2 = (6)^2 + (6)^2 = 36 + 36 = 72`

`AD^2 = (7-1)^2 + (5+1)^2 = (6)^2 + (6)^2 = 36 + 36 = 72`

`AC^2 = (4-1)^2 + (8+1)^2 = (3)^2 + (9)^2 = 9 + 81 = 90`

`BD^2 = (7+2)^2 + (5-2)^2 = (9)^2 + (3)^2 = 81 + 9 = 90`

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

`:. AB=CD` and `BC=AD`

and ` AC^2=BD^2`

`:. AC=BD`

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








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