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.

△ADC and △BDC are right-angled triangles with AD and BC as hypotenuses.
AC² = AB² + DC²
AC² = (5−2)² + (6+1)² = 9 + 49 = 58 sq. unit
BD² = DC² + CB²
BD² = (5−2)² + (−1−6)² = 9 + 49 = 58 sq. unit
Hence, both the diagonals are equal in length.
In △ABO and △CDO
Since, ∠OAB = ∠OCD, ∠OBA = ∠ODC (Both are alternate interior angles of parallel lines) and AB = CD
Therefore △ABO ≅ △CDO
⇒ AO = CO and BO = DO
Therefore, both diagonals bisect each other.