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The points A (0 , 0 , 0) , B (1 , √3 , 0) , C (2 , 0 , 0) and D (1 , 0 , √3) are the vertices of
- a)parallelogram
- b)square
- c)rhombus
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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The points A (0 , 0 , 0) , B (1 , 3, 0) , C (2 , 0 , 0) and D (1 , 0 ,...
Given Points: A (0, 0, 0), B (1, 3, 0), C (2, 0, 0), D (1, 0, 3)
Checking for a parallelogram:
- A parallelogram is a quadrilateral with opposite sides parallel to each other.
- AB is not parallel to CD since AB has a slope of 3 and CD has a slope of -3/2.
- AD is not parallel to BC since AD has a slope of -3 and BC has a slope of 3/2.
- Therefore, the given points do not form a parallelogram.
Checking for a square:
- A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees.
- AB and CD have a length of sqrt(10) but AD and BC have a length of 3.
- Therefore, the given points do not form a square.
Checking for a rhombus:
- A rhombus is a quadrilateral with all sides equal in length but opposite angles are not necessarily equal to 90 degrees.
- AB and CD have a length of sqrt(10) but AD and BC have a length of 3.
- Therefore, the given points do not form a rhombus.
Conclusion:
Since the given points do not form a parallelogram, square, or rhombus, the correct answer is option 'D' (none of these).
Checking for a parallelogram:
- A parallelogram is a quadrilateral with opposite sides parallel to each other.
- AB is not parallel to CD since AB has a slope of 3 and CD has a slope of -3/2.
- AD is not parallel to BC since AD has a slope of -3 and BC has a slope of 3/2.
- Therefore, the given points do not form a parallelogram.
Checking for a square:
- A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees.
- AB and CD have a length of sqrt(10) but AD and BC have a length of 3.
- Therefore, the given points do not form a square.
Checking for a rhombus:
- A rhombus is a quadrilateral with all sides equal in length but opposite angles are not necessarily equal to 90 degrees.
- AB and CD have a length of sqrt(10) but AD and BC have a length of 3.
- Therefore, the given points do not form a rhombus.
Conclusion:
Since the given points do not form a parallelogram, square, or rhombus, the correct answer is option 'D' (none of these).
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The points A (0 , 0 , 0) , B (1 , 3, 0) , C (2 , 0 , 0) and D (1 , 0 ,...
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The points A (0 , 0 , 0) , B (1 , 3, 0) , C (2 , 0 , 0) and D (1 , 0 , 3) are the vertices ofa)parallelogramb)squarec)rhombusd)none of theseCorrect answer is option 'D'. Can you explain this answer?
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