JEE Exam > JEE Questions > If a line intercepted between the coordinate ...
Start Learning for Free
If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:
- a)4x − 3y= 7
- b)3x + 2 y= 18
- c)3x + 8y= 36
- d)x + 3y= 13
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If a line intercepted between the coordinate axes is trisected at a po...
The below figure represents the diagram of the line,
Write the value of the abscissa at point B.
a/3 = 4
a = 12
Write the value of the ordinate at point C.
2b/3 = 3
b = 9/2
Write the equation of the line.
Write the value of the abscissa at point B.
a/3 = 4
a = 12
Write the value of the ordinate at point C.
2b/3 = 3
b = 9/2
Write the equation of the line.
Most Upvoted Answer
If a line intercepted between the coordinate axes is trisected at a po...
To solve this problem, let's first find the coordinates of the other two points that trisect the line.
Since point A (4, 3) is closer to the x-axis, the distance from point A to the x-axis is 3 units. This means that the distance from point A to each of the other two points is also 3 units.
Let's call the first trisecting point B. Since B is 3 units away from A in the x-direction, its x-coordinate is 4 - 3 = 1. Since B is on the x-axis, its y-coordinate is 0. Therefore, the coordinates of B are (1, 0).
Similarly, let's call the second trisecting point C. Since C is 3 units away from A in the y-direction, its y-coordinate is 3 - 3 = 0. Since C is on the y-axis, its x-coordinate is 0. Therefore, the coordinates of C are (0, 0).
Now that we have the coordinates of points A, B, and C, we can find the equation of the line that passes through these points.
We know that the equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line passing through points A and B, we can use the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates of A and B, we get: slope = (0 - 3) / (1 - 4) = 3 / -3 = -1.
Now that we have the slope, we can use the point-slope form of the equation to find the equation of the line: y - y1 = m(x - x1). Plugging in the coordinates of A and the slope, we get: y - 3 = -1(x - 4).
Simplifying, we get: y - 3 = -x + 4.
Finally, rearranging the equation, we get the equation of the line: y = -x + 7.
Therefore, the correct answer is a) 4x - 3y + 21 = 0.
Since point A (4, 3) is closer to the x-axis, the distance from point A to the x-axis is 3 units. This means that the distance from point A to each of the other two points is also 3 units.
Let's call the first trisecting point B. Since B is 3 units away from A in the x-direction, its x-coordinate is 4 - 3 = 1. Since B is on the x-axis, its y-coordinate is 0. Therefore, the coordinates of B are (1, 0).
Similarly, let's call the second trisecting point C. Since C is 3 units away from A in the y-direction, its y-coordinate is 3 - 3 = 0. Since C is on the y-axis, its x-coordinate is 0. Therefore, the coordinates of C are (0, 0).
Now that we have the coordinates of points A, B, and C, we can find the equation of the line that passes through these points.
We know that the equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line passing through points A and B, we can use the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates of A and B, we get: slope = (0 - 3) / (1 - 4) = 3 / -3 = -1.
Now that we have the slope, we can use the point-slope form of the equation to find the equation of the line: y - y1 = m(x - x1). Plugging in the coordinates of A and the slope, we get: y - 3 = -1(x - 4).
Simplifying, we get: y - 3 = -x + 4.
Finally, rearranging the equation, we get the equation of the line: y = -x + 7.
Therefore, the correct answer is a) 4x - 3y + 21 = 0.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer?
Question Description
If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer?.
If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer?.
Solutions for If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a line intercepted between the coordinate axes is trisected at a point A (4, 3), which is nearer to x-axis, then its equation is:a)4x − 3y= 7b)3x + 2 y= 18c)3x + 8y= 36d)x + 3y= 13Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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