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Consider the following equations of straight lines:
Line L1 : 2x - 3y = 5
Line L2 : 3x + 2y = 8
Line L3 : Ax - 6y = 5
Line L4 : 6x - 9y = 6
Which one of the following is the correct statement?
Line L1 : 2x - 3y = 5
Line L2 : 3x + 2y = 8
Line L3 : Ax - 6y = 5
Line L4 : 6x - 9y = 6
Which one of the following is the correct statement?
- a)L1 is parallel to L2 and L1 is perpendicular to L3
- b)L2 is parallel to L4 and L2 is perpendicular to L1
- c)L4 is perpendicular to L2 and L4 is parallel to L3
- d)L3 is perpendicular to L4 and L3 is parallel to L2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following equations of straight lines:Line L1 : 2x - 3y =...
Understanding Line Relationships
To determine the relationships between the lines, we need to analyze their slopes. Lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1.
Finding Slopes of the Lines
1. Line L1:
2x - 3y = 5
Rearranging gives:
y = (2/3)x - 5/3
Slope (m1) = 2/3
2. Line L2:
3x + 2y = 8
Rearranging gives:
y = (-3/2)x + 4
Slope (m2) = -3/2
3. Line L3:
Ax - 6y = 5
Rearranging gives:
y = (A/6)x - 5/6
Slope (m3) = A/6
4. Line L4:
6x - 9y = 6
Rearranging gives:
y = (2/3)x - 2/3
Slope (m4) = 2/3
Analyzing Relationships
- Parallel Lines:
L1 (slope = 2/3) and L4 (slope = 2/3) are parallel because they share the same slope.
- Perpendicular Lines:
To check if L2 and L4 are perpendicular, we multiply their slopes:
m2 * m4 = (-3/2) * (2/3) = -1.
Thus, L2 and L4 are perpendicular.
- L3's Relationship:
For L3 to be perpendicular to L4, we need m3 to equal -1/m4. However, without knowing A, we can't definitively conclude this.
Conclusion
After analyzing the slopes:
- L4 is confirmed to be perpendicular to L2.
- L4 is parallel to L1.
Given these relationships, option 'C' is indeed correct because L4 is perpendicular to L2 and parallel to L3 when A = -4.
To determine the relationships between the lines, we need to analyze their slopes. Lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1.
Finding Slopes of the Lines
1. Line L1:
2x - 3y = 5
Rearranging gives:
y = (2/3)x - 5/3
Slope (m1) = 2/3
2. Line L2:
3x + 2y = 8
Rearranging gives:
y = (-3/2)x + 4
Slope (m2) = -3/2
3. Line L3:
Ax - 6y = 5
Rearranging gives:
y = (A/6)x - 5/6
Slope (m3) = A/6
4. Line L4:
6x - 9y = 6
Rearranging gives:
y = (2/3)x - 2/3
Slope (m4) = 2/3
Analyzing Relationships
- Parallel Lines:
L1 (slope = 2/3) and L4 (slope = 2/3) are parallel because they share the same slope.
- Perpendicular Lines:
To check if L2 and L4 are perpendicular, we multiply their slopes:
m2 * m4 = (-3/2) * (2/3) = -1.
Thus, L2 and L4 are perpendicular.
- L3's Relationship:
For L3 to be perpendicular to L4, we need m3 to equal -1/m4. However, without knowing A, we can't definitively conclude this.
Conclusion
After analyzing the slopes:
- L4 is confirmed to be perpendicular to L2.
- L4 is parallel to L1.
Given these relationships, option 'C' is indeed correct because L4 is perpendicular to L2 and parallel to L3 when A = -4.
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Community Answer
Consider the following equations of straight lines:Line L1 : 2x - 3y =...
Line L1 : 2x - 3y = 5
Line L2 : 3x + 2y = 8
Line L3 : 4x - 6y = 5
Line L4 : 6x - 9y = 6
∴
and
∴ L1, L3, L4 are parallel to each other and perpendicular to L2.
Line L2 : 3x + 2y = 8
Line L3 : 4x - 6y = 5
Line L4 : 6x - 9y = 6
∴
and
∴ L1, L3, L4 are parallel to each other and perpendicular to L2.
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Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer?
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Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer?.
Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer?.
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Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following equations of straight lines:Line L1 : 2x - 3y = 5Line L2 : 3x + 2y = 8Line L3 : Ax - 6y = 5Line L4 : 6x - 9y = 6Which one of the following is the correct statement?a)L1 is parallel to L2 and L1 is perpendicular to L3b)L2 is parallel to L4 and L2 is perpendicular to L1c)L4 is perpendicular to L2 and L4 is parallel to L3d)L3 is perpendicular to L4 and L3 is parallel to L2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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