Class 11 Exam > Class 11 Questions > A line segment AB of length 2 moves with it's...
Start Learning for Free
A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is?
Verified Answer
A line segment AB of length 2 moves with it's ends on the axes .the lo...
The locus of a point is the set of all points that the point can occupy over a period of time or under certain conditions. In this case, the point P is dividing the line segment AB into two parts of equal length, with the ratio 1:1.
If the line segment AB is moving with its ends on the axes, and point P is dividing it into two parts of equal length, then the locus of point P will be a line that is perpendicular to AB and passes through the midpoint of AB.
To find the length of the line segment AB, you can use the Pythagorean Theorem:
AB = √(x2 - x1)2 + (y2 - y1)2
= √(02 - 02)2 + (02 - (-2))2
= √(00)2 + (2)2
= √(4)
= 2
The midpoint of AB is the point that divides the line segment into two parts of equal length, and it is located at the coordinates (0, 0).
So, the locus of point P will be a line that is perpendicular to AB and passes through the midpoint of AB, which is located at (0, 0). This line will be a straight line that is parallel to one of the axes.
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
A line segment AB of length 2 moves with it's ends on the axes .the lo...
Locating the Locus of a Point Dividing a Line Segment in 1:1 Ratio
The locus of the point P which divides the line segment AB in a 1:1 ratio can be determined by following a few steps.
Given Information:
- Length of line segment AB = 2
- The ends of the line segment AB are on the axes
Finding the Locus:
- Let the coordinates of point A be (a, 0) and point B be (0, b) on the axes
- Since the point P divides the line segment AB in a 1:1 ratio, its coordinates can be expressed as ((a + 0)/2, (0 + b)/2) = (a/2, b/2)
- Using the distance formula, the length of the line segment AB is given by √((a-0)^2 + (0-b)^2) = 2
- Substituting the coordinates of point P in the distance formula and equating it to 2, we get √((a/2-0)^2 + (b/2-0)^2) = 2
- Simplifying the equation gives us √(a^2 + b^2) = 2√2
- Squaring both sides gives us a^2 + b^2 = 8
Conclusion:
The locus of the point P which divides the line segment AB in a 1:1 ratio is a circle centered at the origin (0, 0) with a radius of √8 or 2√2. The equation of the locus is a^2 + b^2 = 8.
The locus of the point P which divides the line segment AB in a 1:1 ratio can be determined by following a few steps.
Given Information:
- Length of line segment AB = 2
- The ends of the line segment AB are on the axes
Finding the Locus:
- Let the coordinates of point A be (a, 0) and point B be (0, b) on the axes
- Since the point P divides the line segment AB in a 1:1 ratio, its coordinates can be expressed as ((a + 0)/2, (0 + b)/2) = (a/2, b/2)
- Using the distance formula, the length of the line segment AB is given by √((a-0)^2 + (0-b)^2) = 2
- Substituting the coordinates of point P in the distance formula and equating it to 2, we get √((a/2-0)^2 + (b/2-0)^2) = 2
- Simplifying the equation gives us √(a^2 + b^2) = 2√2
- Squaring both sides gives us a^2 + b^2 = 8
Conclusion:
The locus of the point P which divides the line segment AB in a 1:1 ratio is a circle centered at the origin (0, 0) with a radius of √8 or 2√2. The equation of the locus is a^2 + b^2 = 8.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is?
Question Description
A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is?.
A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is?.
Solutions for A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? defined & explained in the simplest way possible. Besides giving the explanation of
A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is?, a detailed solution for A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? has been provided alongside types of A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? theory, EduRev gives you an
ample number of questions to practice A line segment AB of length 2 moves with it's ends on the axes .the locus of the point P which divides the segment in the ratio 1:1 is? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 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