17. Show that the points A(0, 0) , B(6, 0) , D(9, 4) and C(3, 4) are the vertices of a parallelogram taken in order. [3]
Answers
Solution :-
checking length of sides of ll gm ABDC by distance formula we get,
→ AB = √[(0 - 6)² + (0 - 0)²] = √(36 + 0) = 6 unit
→ BD = [(6 - 9)² + (0 - 4)²] = √(9 + 16) = 5 unit
→ DC = √[(9 - 3)² + (4 - 4)²] = √(36 + 0) = 6 unit
→ CA = [(3 - 0)² + (4 - 0)²] = √(9 + 16) = 5 unit
now, checking mid points of diagonals AD and BC we get,
→ Coordinates of the midpoint of AD = (0 + 9)/2 and (0 + 4)/2 = (9/2, 2)
→ Coordinates of the midpoint of BC = (6 + 3)/2 and (0 + 4)/2 = (9/2, 2)
as we can see that,
- AB = DC
- BD = CA
- Opposite sides of a parallelogram are equal .
and,
- Coordinates of midpoint of AD = Coordinates of midpoint of BC .
- Diagonals of a parallelogram bisect each other .
Therefore, we can conclude that, ABDC is a parallelogram .
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