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The given points are A(2,1), B(5,2), C(6,4) and D(3,3)
But diagonal AC is not equal to diagonal BD.
AB = √( 5 - 2 )² + ( 2 - 1 )² = √(3)² + (1)²
= √9 + 1 = √10 units
BC = √( 6 - 2 )² + (4 - 2)² = √(1)² + (2)²
= √1 + 4 = √ 5 units
CD = √( 3 - 6 )² + ( 3 - 4 )² = √(-3)² + (-1)²
= √9 + 1 = √10 units
AD = √( 3 - 2 )² + ( 3 + 1 )² = √(1)² + (2)²
= √1 + 4 = √5 units
Thus, AB = CD = √10 units and BC = AD = √5 units.
So, quadrilateral ABCD is a parallelogram.
Also,
AC = √( 6 - 2 )² + ( 4 - 1 )² = √(4)² + (3)²
= √16 + 9
= √25 = √5 units
BD = √( 3 - 5)² + ( 3 - 2 )² = √(-2)² + (1)²
= √4 + 1
= √5 units
Hence, the given points do not form a rectangle.
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