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Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square?
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Understanding Distance from the Origin
The distance of a point from the origin in a Cartesian coordinate system is calculated using the Pythagorean theorem. For a point P with coordinates (a, b), the distance (d) from the origin (0, 0) is given by:
- d = √(a² + b²)
This formula arises because the distance forms a right triangle where 'a' and 'b' are the lengths of the two sides.
Distance Between Two Points
To find the distance between two points A (x1, y1) and B (x2, y2), we again apply the Pythagorean theorem. The distance (D) can be expressed as:
- D = √((x2 - x1)² + (y2 - y1)²)
This formula calculates the straight-line distance between the two points in a 2D plane. Here’s how it works:
- The difference (x2 - x1) represents the horizontal distance between the points.
- The difference (y2 - y1) represents the vertical distance.
- Squaring these differences gives the area of the respective squares, and taking the square root provides the actual distance.
Key Takeaways
- The distance from the origin can be visualized as the hypotenuse of a right triangle formed with the axes.
- The distance between two points encapsulates the changes in both the x and y coordinates, resulting in a straight-line measurement.
Understanding these principles is essential for problems involving geometry and coordinate systems, especially in examinations like UPSC.
The distance of a point from the origin in a Cartesian coordinate system is calculated using the Pythagorean theorem. For a point P with coordinates (a, b), the distance (d) from the origin (0, 0) is given by:
- d = √(a² + b²)
This formula arises because the distance forms a right triangle where 'a' and 'b' are the lengths of the two sides.
Distance Between Two Points
To find the distance between two points A (x1, y1) and B (x2, y2), we again apply the Pythagorean theorem. The distance (D) can be expressed as:
- D = √((x2 - x1)² + (y2 - y1)²)
This formula calculates the straight-line distance between the two points in a 2D plane. Here’s how it works:
- The difference (x2 - x1) represents the horizontal distance between the points.
- The difference (y2 - y1) represents the vertical distance.
- Squaring these differences gives the area of the respective squares, and taking the square root provides the actual distance.
Key Takeaways
- The distance from the origin can be visualized as the hypotenuse of a right triangle formed with the axes.
- The distance between two points encapsulates the changes in both the x and y coordinates, resulting in a straight-line measurement.
Understanding these principles is essential for problems involving geometry and coordinate systems, especially in examinations like UPSC.
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Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square?
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Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square?.
Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion the distance of p a ,b from the origin is a square + b square is and the distance between two points a x1 upon y1 and b x ^ y2 is under root x minus x square + y2 - y1 bra square?.
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