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If l is any given line and P is any point not lying on l, then the number of parallel lines that can be drawn through P, parallel to l would be :
- a)One
- b)Two
- c)Infinite
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If lis any given line and P is any point not lying on l, then the numb...
Draw a line l and a point P not lying on l.
Now, we can draw a straight line parallel to l which passes through P.
Clearly from the figure, only one line can be drawn which is parallel to l and passes through P.
Most Upvoted Answer
If lis any given line and P is any point not lying on l, then the numb...
Explanation:
When a line L is given and a point P is given that does not lie on line L, we need to determine the number of parallel lines that can be drawn through point P, parallel to line L.
Key Points:
To understand the solution, we need to remember the following key points:
1. Parallel lines are lines that never intersect and have the same slope.
2. If two lines are parallel, their slopes are equal.
3. The slope of a line can be determined by any two points on the line.
Solution:
To determine the number of parallel lines that can be drawn through point P, parallel to line L, we need to consider the slope of line L.
Case 1: Line L is vertical:
If line L is vertical, it does not have a slope. In this case, there are no parallel lines that can be drawn through point P, parallel to line L.
Case 2: Line L is not vertical:
If line L is not vertical, it has a slope. Let's consider two points A and B on line L. The slope of line L can be determined using these two points.
Now, let's consider a line M passing through point P. To be parallel to line L, the slope of line M should be equal to the slope of line L.
Key Point 1:
A line passing through point P will have the same slope as line L if and only if it passes through point P and another point on line L.
Key Point 2:
Given any point, there is exactly one line that can be drawn through that point parallel to a given line.
Therefore, there is only one parallel line that can be drawn through point P, parallel to line L.
Conclusion:
The correct answer is option 'A' - One. There is only one parallel line that can be drawn through point P, parallel to line L.
When a line L is given and a point P is given that does not lie on line L, we need to determine the number of parallel lines that can be drawn through point P, parallel to line L.
Key Points:
To understand the solution, we need to remember the following key points:
1. Parallel lines are lines that never intersect and have the same slope.
2. If two lines are parallel, their slopes are equal.
3. The slope of a line can be determined by any two points on the line.
Solution:
To determine the number of parallel lines that can be drawn through point P, parallel to line L, we need to consider the slope of line L.
Case 1: Line L is vertical:
If line L is vertical, it does not have a slope. In this case, there are no parallel lines that can be drawn through point P, parallel to line L.
Case 2: Line L is not vertical:
If line L is not vertical, it has a slope. Let's consider two points A and B on line L. The slope of line L can be determined using these two points.
Now, let's consider a line M passing through point P. To be parallel to line L, the slope of line M should be equal to the slope of line L.
Key Point 1:
A line passing through point P will have the same slope as line L if and only if it passes through point P and another point on line L.
Key Point 2:
Given any point, there is exactly one line that can be drawn through that point parallel to a given line.
Therefore, there is only one parallel line that can be drawn through point P, parallel to line L.
Conclusion:
The correct answer is option 'A' - One. There is only one parallel line that can be drawn through point P, parallel to line L.
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If lis any given line and P is any point not lying on l, then the number of parallel lines that can be drawnthrough P, parallel to lwould be :a)Oneb)Twoc)Infinited)None of theseCorrect answer is option 'A'. Can you explain this answer?
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