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What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?
- a)4 x + 3 y + 2 = 0
- b)4 x - y + 2 = 0
- c)4 x - 3 y - 2 = 0
- d)4x-3y+2 = 0
Correct answer is option 'D'. Can you explain this answer?
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What is the equation of the straight line which passes through the poi...
Intersecting lines are : x+2y = 5 & 3x + 7y = 17
On solving these we get : x = 1 & y = 2
Equation of perpendicular line is
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What is the equation of the straight line which passes through the poi...
To find the equation of the straight line that passes through the point of intersection of two given lines and is perpendicular to a third line, we can follow these steps:
Step 1: Find the point of intersection of the given lines.
Step 2: Determine the slope of the third line.
Step 3: Find the negative reciprocal of the slope from Step 2 to get the slope of the desired line.
Step 4: Use the slope from Step 3 and the point of intersection from Step 1 to write the equation of the desired line.
Let's solve the problem using these steps:
Step 1: Finding the point of intersection of the given lines:
The given lines are:
1) x - 2y = 5
2) 3x - 7y = 17
We can solve these equations simultaneously to find the point of intersection.
Multiplying the first equation by 3 and the second equation by 1, we get:
3(x - 2y) = 3(5) --> 3x - 6y = 15
3x - 7y = 17
Subtracting the second equation from the first equation:
(3x - 6y) - (3x - 7y) = 15 - 17
y = 2
Substituting y = 2 into the first equation:
x - 2(2) = 5
x - 4 = 5
x = 9
Therefore, the point of intersection is (9, 2).
Step 2: Determining the slope of the third line:
The third line is given as:
3x + 4y = 10
We can rewrite this equation in slope-intercept form (y = mx + c), where m is the slope:
4y = -3x + 10
y = (-3/4)x + (10/4)
y = (-3/4)x + (5/2)
The slope of the third line is -3/4.
Step 3: Finding the negative reciprocal of the slope from Step 2:
The negative reciprocal of -3/4 is 4/3.
Step 4: Using the slope from Step 3 and the point of intersection from Step 1 to write the equation of the desired line:
Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the point of intersection and m is the slope:
y - 2 = (4/3)(x - 9)
3y - 6 = 4x - 36
4x - 3y + 30 = 0
Therefore, the equation of the straight line that passes through the point of intersection of the given lines and is perpendicular to the third line is 4x - 3y + 30 = 0.
Hence, the correct answer is option D) 4x - 3y + 30 = 0.
Step 1: Find the point of intersection of the given lines.
Step 2: Determine the slope of the third line.
Step 3: Find the negative reciprocal of the slope from Step 2 to get the slope of the desired line.
Step 4: Use the slope from Step 3 and the point of intersection from Step 1 to write the equation of the desired line.
Let's solve the problem using these steps:
Step 1: Finding the point of intersection of the given lines:
The given lines are:
1) x - 2y = 5
2) 3x - 7y = 17
We can solve these equations simultaneously to find the point of intersection.
Multiplying the first equation by 3 and the second equation by 1, we get:
3(x - 2y) = 3(5) --> 3x - 6y = 15
3x - 7y = 17
Subtracting the second equation from the first equation:
(3x - 6y) - (3x - 7y) = 15 - 17
y = 2
Substituting y = 2 into the first equation:
x - 2(2) = 5
x - 4 = 5
x = 9
Therefore, the point of intersection is (9, 2).
Step 2: Determining the slope of the third line:
The third line is given as:
3x + 4y = 10
We can rewrite this equation in slope-intercept form (y = mx + c), where m is the slope:
4y = -3x + 10
y = (-3/4)x + (10/4)
y = (-3/4)x + (5/2)
The slope of the third line is -3/4.
Step 3: Finding the negative reciprocal of the slope from Step 2:
The negative reciprocal of -3/4 is 4/3.
Step 4: Using the slope from Step 3 and the point of intersection from Step 1 to write the equation of the desired line:
Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the point of intersection and m is the slope:
y - 2 = (4/3)(x - 9)
3y - 6 = 4x - 36
4x - 3y + 30 = 0
Therefore, the equation of the straight line that passes through the point of intersection of the given lines and is perpendicular to the third line is 4x - 3y + 30 = 0.
Hence, the correct answer is option D) 4x - 3y + 30 = 0.
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What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer?
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What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. 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 What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer?.
What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. 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 What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x+4y= 10?a)4 x + 3 y + 2 = 0b)4 x - y +2 = 0c)4 x - 3 y - 2 = 0d)4x-3y+2 = 0Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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