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How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?
- a)0
- b)Infinite
- c)2
- d)1
Correct answer is option 'D'. Can you explain this answer?
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How many parallel lines can be drawn parallel to a given line L and pa...
Only one line can be drawn parallel to a given line and passing through a fixed point.
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How many parallel lines can be drawn parallel to a given line L and pa...
Understanding Parallel Lines
In geometry, parallel lines are defined as lines in a plane that never meet; they are always the same distance apart. Given this definition, let’s explore the scenario presented in the question.
Given Line L and Fixed Point P
- When you have a specific line L and a fixed point P not on line L, you can draw exactly one line through point P that is parallel to line L.
- This is a fundamental property of Euclidean geometry, which states that through a point not on a line, there is exactly one line that can be drawn parallel to the given line.
Why Only One Parallel Line?
- If you attempt to draw more than one line through point P that is parallel to line L, those lines would eventually intersect line L, contradicting the definition of parallel lines.
- Therefore, it is geometrically impossible to have two distinct lines through a single point that maintain the property of being parallel to another line.
Conclusion
- The correct answer to the number of parallel lines that can be drawn through a fixed point P, parallel to line L, is indeed 1.
- This reinforces the unique relationship between a line and a point not on that line within Euclidean geometry.
In geometry, parallel lines are defined as lines in a plane that never meet; they are always the same distance apart. Given this definition, let’s explore the scenario presented in the question.
Given Line L and Fixed Point P
- When you have a specific line L and a fixed point P not on line L, you can draw exactly one line through point P that is parallel to line L.
- This is a fundamental property of Euclidean geometry, which states that through a point not on a line, there is exactly one line that can be drawn parallel to the given line.
Why Only One Parallel Line?
- If you attempt to draw more than one line through point P that is parallel to line L, those lines would eventually intersect line L, contradicting the definition of parallel lines.
- Therefore, it is geometrically impossible to have two distinct lines through a single point that maintain the property of being parallel to another line.
Conclusion
- The correct answer to the number of parallel lines that can be drawn through a fixed point P, parallel to line L, is indeed 1.
- This reinforces the unique relationship between a line and a point not on that line within Euclidean geometry.
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How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer?
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How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer?.
How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many parallel lines can be drawn parallel to a given line L and passing through a fixed point P?a)0b)Infinitec)2d)1Correct answer is option 'D'. Can you explain this answer?.
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