UPSC Exam > UPSC Questions > Find the equation of a line passing through t...
Start Learning for Free
Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.?
Most Upvoted Answer
Find the equation of a line passing through the point of intersection ...
Step 1: Find the intersection of the lines
To find the point of intersection of the lines given by:
1. 2x + y = 8
2. x - y = 10
We can solve these equations simultaneously.
- From equation 2, express y in terms of x:
- y = x - 10
- Substitute y into equation 1:
- 2x + (x - 10) = 8
- 3x - 10 = 8
- 3x = 18
- x = 6
- Substitute x back to find y:
- y = 6 - 10 = -4
Thus, the point of intersection is (6, -4).
Step 2: Determine the slope of perpendicular line
The line that is perpendicular to another line has a slope that is the negative reciprocal of the original line's slope.
The equation 3x + 4y = 2012 can be rewritten in slope-intercept form (y = mx + b):
- Rearranging gives: 4y = -3x + 2012
- Therefore, y = (-3/4)x + 503
The slope (m) of this line is -3/4.
Thus, the slope of the line we need to find (perpendicular line) is:
- m_perpendicular = 4/3
Step 3: Formulate the equation of the new line
Using the point-slope form of the equation of a line (y - y1 = m(x - x1)):
- Point (x1, y1) = (6, -4)
- Slope (m) = 4/3
The equation becomes:
- y - (-4) = (4/3)(x - 6)
This simplifies to:
- y + 4 = (4/3)x - 8
- y = (4/3)x - 12
Final Equation
The equation of the line passing through the intersection point and perpendicular to the given line is:
- y = (4/3)x - 12.
To find the point of intersection of the lines given by:
1. 2x + y = 8
2. x - y = 10
We can solve these equations simultaneously.
- From equation 2, express y in terms of x:
- y = x - 10
- Substitute y into equation 1:
- 2x + (x - 10) = 8
- 3x - 10 = 8
- 3x = 18
- x = 6
- Substitute x back to find y:
- y = 6 - 10 = -4
Thus, the point of intersection is (6, -4).
Step 2: Determine the slope of perpendicular line
The line that is perpendicular to another line has a slope that is the negative reciprocal of the original line's slope.
The equation 3x + 4y = 2012 can be rewritten in slope-intercept form (y = mx + b):
- Rearranging gives: 4y = -3x + 2012
- Therefore, y = (-3/4)x + 503
The slope (m) of this line is -3/4.
Thus, the slope of the line we need to find (perpendicular line) is:
- m_perpendicular = 4/3
Step 3: Formulate the equation of the new line
Using the point-slope form of the equation of a line (y - y1 = m(x - x1)):
- Point (x1, y1) = (6, -4)
- Slope (m) = 4/3
The equation becomes:
- y - (-4) = (4/3)(x - 6)
This simplifies to:
- y + 4 = (4/3)x - 8
- y = (4/3)x - 12
Final Equation
The equation of the line passing through the intersection point and perpendicular to the given line is:
- y = (4/3)x - 12.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.?
Question Description
Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.?.
Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.?.
Solutions for Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? defined & explained in the simplest way possible. Besides giving the explanation of
Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.?, a detailed solution for Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? has been provided alongside types of Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? theory, EduRev gives you an
ample number of questions to practice Find the equation of a line passing through the point of intersection of the lines 2x + y = 8 and x - y = 10 and is perpendicular to 3x + 4y 2012-0.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup