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Coordinate Geometry
Question
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Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

Answer

                            

 

    AC2 = ( 5 -2 )2 + ( 6 + 1 )2 

          = 9 + 49 

          = 58 sq.unit

BD2 = ( 5 - 2 )2 + ( -1 -6 )2 

      = 9 + 49

      = 58 sq unit

Diagonals of parallelogram are equal so rectangle.

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Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.