The points A(1,1), B(7,-3), C(12,2) and D(7,21) are the vertices of the quadrilateral ABCD. Determine whether ABCD is a rectangle or not.
Answers
Given :- The points A(1,1), B(7,-3), C(12,2) and D(7,21) are the vertices of the quadrilateral ABCD.
To Find :- Determine whether ABCD is a rectangle or not. ?
Solution :-
→ AB = √[(7 - 1)² + (-3 - 1)²] = √{6² + (-4)²} = √(36 + 16) = √52 = 2√13
→ BC = √[(12 - 7)² + (2 - -3)²] = √{5² + 5²} = √(25 + 25) = √50 = 5√2
→ CD = √[(7 - 12)² + (21 - 2)²] = √{(-5)² + (19)²} = √(25 + 361) = √386 .
→ DA = √[(1 - 7)² + (1 - 21)²] = √{(-6)² + (-20)²} = √(36 + 400) = √436 = 2√109
since ,
- AB ≠ CD .
- BC ≠ DA .
- Opposite sides are not equal .
therefore, we can conclude that, the given quadrilateral ABCD is not a rectangle .
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