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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?
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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.
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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.
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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?
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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?.
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