JEE Exam > JEE Questions > A line inclined at an angle of 135∘ to the x-...
Start Learning for Free
A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)?
Most Upvoted Answer
A line inclined at an angle of 135∘ to the x-axis passes through the p...
Given:
- A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4).
- AP = AQ = 22.
To Find:
The coordinates of points P and Q.
Solution:
Step 1: Finding the Slope:
The line is inclined at an angle of 135∘ to the x-axis, which means it makes an angle of (180∘ - 135∘) = 45∘ with the positive x-axis. This angle corresponds to the slope of the line.
The slope of the line is given by the tangent of this angle:
m = tan(45∘) = 1
Step 2: Finding the Equation of the Line:
We have the slope (m = 1) and a point on the line (A = (3,4)). We can use the point-slope form to find the equation of the line.
Using the point-slope form:
y - y1 = m(x - x1)
y - 4 = 1(x - 3)
y - 4 = x - 3
y = x + 1
So, the equation of the line passing through A(3,4) is y = x + 1.
Step 3: Finding Points P and Q:
We are given that AP = AQ = 22.
Using the distance formula:
√[(x2 - x1)^2 + (y2 - y1)^2] = 22
For point P:
√[(-1 - 3)^2 + (-0 - 4)^2] = 22
√[16 + 16] = 22
√32 = 22
32 = 484
This is not true, so point P is not correct.
For point Q:
√[(5 - 3)^2 + (2 - 4)^2] = 22
√[4 + 4] = 22
√8 = 22
8 = 484
This is not true, so point Q is not correct.
Conclusion:
There is an error in the given coordinates of points P and Q. None of the given options (-1, -0), (5, 2), (1, -6), (1, 6), (-5, 2), (5, -2) satisfy the condition AP = AQ = 22.
Please check the given coordinates and provide the correct coordinates for points P and Q.
- A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4).
- AP = AQ = 22.
To Find:
The coordinates of points P and Q.
Solution:
Step 1: Finding the Slope:
The line is inclined at an angle of 135∘ to the x-axis, which means it makes an angle of (180∘ - 135∘) = 45∘ with the positive x-axis. This angle corresponds to the slope of the line.
The slope of the line is given by the tangent of this angle:
m = tan(45∘) = 1
Step 2: Finding the Equation of the Line:
We have the slope (m = 1) and a point on the line (A = (3,4)). We can use the point-slope form to find the equation of the line.
Using the point-slope form:
y - y1 = m(x - x1)
y - 4 = 1(x - 3)
y - 4 = x - 3
y = x + 1
So, the equation of the line passing through A(3,4) is y = x + 1.
Step 3: Finding Points P and Q:
We are given that AP = AQ = 22.
Using the distance formula:
√[(x2 - x1)^2 + (y2 - y1)^2] = 22
For point P:
√[(-1 - 3)^2 + (-0 - 4)^2] = 22
√[16 + 16] = 22
√32 = 22
32 = 484
This is not true, so point P is not correct.
For point Q:
√[(5 - 3)^2 + (2 - 4)^2] = 22
√[4 + 4] = 22
√8 = 22
8 = 484
This is not true, so point Q is not correct.
Conclusion:
There is an error in the given coordinates of points P and Q. None of the given options (-1, -0), (5, 2), (1, -6), (1, 6), (-5, 2), (5, -2) satisfy the condition AP = AQ = 22.
Please check the given coordinates and provide the correct coordinates for points P and Q.
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
A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)?
Question Description
A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)?.
A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)?.
Solutions for A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? 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 A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? defined & explained in the simplest way possible. Besides giving the explanation of
A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)?, a detailed solution for A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? has been provided alongside types of A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? theory, EduRev gives you an
ample number of questions to practice A line inclined at an angle of 135∘ to the x-axis passes through the point A(3,4). There are two points P and Q on the line such that AP=AQ=22. The co-ordinates of P and Q are respectively (−1,−0) and (5,2) (1,−6) and (−5,2) (1,6) and (5,−2) (1,6) and (5,2)? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup