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Prove:The point (2,-2),(8,4),(5,7)& (-1,1) are the angular points of a rectangle

Prove:The point (2,-2),(8,4),(5,7)& (-1,1) are the angular points of a rectangle

Grade:11

1 Answers

Arun
25763 Points
4 years ago
 
Let these points are A,B,C,D respectively.
Hence
From distance formula
distance AB =52^(1/2)
distance CD = 52 ^(1/2)
distance BC = 18^(1/2)
distance AD = 18^(1/2)
Now AB = CD & BC = AD
One property of rectangle is that its disgonal are equal in length.
Now 
length AC = 90^(1/2)
length BD = 90^(1/2)
Now AC = BD also.
Hence this is a rectangle

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