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Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is
- a)7x + y - 21 = 0
- b)x + 7y + 21 = 0
- c)2x + y - 8 = 0
- d)x + 2y + 8 = 0
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two straight lines passing through the point A(3,2) cut the line 2y = ...
Coordinates of Q are (3,0) & it passes through PQ.
Putting the values of(x=3) & (y=0) m options we get:
Equation of line PQ = 7x + y - 21 = 0
Putting the values of(x=3) & (y=0) m options we get:
Equation of line PQ = 7x + y - 21 = 0
Most Upvoted Answer
Two straight lines passing through the point A(3,2) cut the line 2y = ...
Given Information:
- Point A(3,2)
- Line 2y = x - 3
- Perpendicular lines passing through A(3,2) cutting the given line and x-axis at points P and Q
Solution:
Finding the Slope of the Given Line:
- The given line is in the form 2y = x - 3, which can be rewritten as y = (1/2)x - 3/2
- The slope of this line is 1/2
Finding the Slope of the Perpendicular Lines:
- The product of slopes for perpendicular lines is -1
- So, the slope of the perpendicular lines passing through A(3,2) will be -2
Equation of Line Passing Through A(3,2) with Slope -2:
- Using the point-slope form of the line equation: y - y₁ = m(x - x₁), where (x₁, y₁) = (3,2) and m = -2
- y - 2 = -2(x - 3)
- y - 2 = -2x + 6
- 2x + y - 8 = 0
Equation of Line PQ:
- Since P lies on the given line 2y = x - 3 and Q lies on the x-axis (y = 0), we can find the coordinates of P and Q
- Substitute y = 0 in 2y = x - 3 to find Q: x = 3
- So, Q(3,0) and P satisfies the equation 2x + y - 8 = 0: 2(3) + 0 - 8 = 6 - 8 = -2
- So, P(3,-2)
- Therefore, the equation of line PQ passing through P and Q is 2x + y - 8 = 0
Therefore, the correct answer is option 'A'.
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Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer?
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Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer?.
Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two straight lines passing through the point A(3,2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ isa)7x + y - 21 = 0b)x + 7y + 21 = 0c)2x + y - 8 = 0d)x + 2y + 8 = 0Correct answer is option 'A'. Can you explain this answer?.
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