If A Young Point M Lies On Y Axis Then Its Co-ordinate​

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Introduction

In mathematics, the coordinate system is a fundamental concept used to represent points and locations in a two-dimensional or three-dimensional space. The coordinate system is based on the concept of axes, which are imaginary lines that intersect at a point called the origin. In this article, we will explore the concept of the coordinate system, specifically focusing on the case where a young point M lies on the y-axis.

What is the Y-Axis?

The y-axis is one of the two axes in a two-dimensional coordinate system. It is an imaginary line that extends infinitely in both directions and is perpendicular to the x-axis. The y-axis is used to measure the vertical distance of a point from the origin. In a standard coordinate system, the y-axis is represented by the letter 'y' and is usually drawn as a vertical line.

Coordinate Notation

In a coordinate system, each point is represented by a pair of numbers, known as the x-coordinate and the y-coordinate. The x-coordinate represents the horizontal distance of the point from the origin, while the y-coordinate represents the vertical distance. In the case where a point M lies on the y-axis, the x-coordinate is always zero, and the y-coordinate represents the vertical distance of the point from the origin.

Finding the Coordinate of a Point on the Y-Axis

To find the coordinate of a point M that lies on the y-axis, we need to determine the value of the y-coordinate. Since the point lies on the y-axis, the x-coordinate is always zero. Therefore, the coordinate of the point M is (0, y), where y is the value of the y-coordinate.

Example

Suppose we have a point M that lies on the y-axis at a distance of 5 units from the origin. To find the coordinate of the point M, we need to determine the value of the y-coordinate. Since the point lies on the y-axis, the x-coordinate is always zero. Therefore, the coordinate of the point M is (0, 5).

Properties of Points on the Y-Axis

Points on the y-axis have some unique properties that distinguish them from points on the x-axis. Some of the key properties of points on the y-axis include:

  • Zero x-coordinate: The x-coordinate of a point on the y-axis is always zero.
  • Non-zero y-coordinate: The y-coordinate of a point on the y-axis is always non-zero.
  • Vertical distance: The y-coordinate of a point on the y-axis represents the vertical distance of the point from the origin.

Applications of Points on the Y-Axis

Points on the y-axis have numerous applications in mathematics, science, and engineering. Some of the key applications of points on the y-axis include:

  • Graphing functions: Points on the y-axis are used to graph functions in a coordinate system.
  • Analyzing data: Points on the y-axis are used to analyze data in a coordinate system.
  • Solving equations: Points on the y-axis are used to solve equations in a coordinate system.

Conclusion

In conclusion, the coordinate system is a fundamental concept used to represent points and locations in a two-dimensional or three-dimensional space. Points on the y-axis have unique properties that distinguish them from points on the x-axis. Understanding the properties and applications of points on the y-axis is essential for solving problems in mathematics, science, and engineering.

Frequently Asked Questions

Q: What is the y-axis?

A: The y-axis is one of the two axes in a two-dimensional coordinate system. It is an imaginary line that extends infinitely in both directions and is perpendicular to the x-axis.

Q: What is the coordinate notation for a point on the y-axis?

A: The coordinate notation for a point on the y-axis is (0, y), where y is the value of the y-coordinate.

Q: What are the properties of points on the y-axis?

A: Points on the y-axis have the following properties:

  • Zero x-coordinate
  • Non-zero y-coordinate
  • Vertical distance

Q: What are the applications of points on the y-axis?

A: Points on the y-axis have numerous applications in mathematics, science, and engineering, including graphing functions, analyzing data, and solving equations.

References

Q&A: Coordinate System and Points on the Y-Axis

Q: What is the origin in a coordinate system?

A: The origin is the point where the x-axis and y-axis intersect. It is represented by the coordinates (0, 0).

Q: What is the difference between the x-axis and y-axis?

A: The x-axis is an imaginary line that extends infinitely in both directions and is used to measure the horizontal distance of a point from the origin. The y-axis is an imaginary line that extends infinitely in both directions and is used to measure the vertical distance of a point from the origin.

Q: What is the coordinate notation for a point on the x-axis?

A: The coordinate notation for a point on the x-axis is (x, 0), where x is the value of the x-coordinate.

Q: What is the coordinate notation for a point on the y-axis?

A: The coordinate notation for a point on the y-axis is (0, y), where y is the value of the y-coordinate.

Q: What is the distance formula in a coordinate system?

A: The distance formula in a coordinate system is:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between two points (x1, y1) and (x2, y2).

Q: How do you find the midpoint of two points in a coordinate system?

A: To find the midpoint of two points (x1, y1) and (x2, y2), you can use the following formula:

(x, y) = ((x1 + x2)/2, (y1 + y2)/2)

Q: What is the slope of a line in a coordinate system?

A: The slope of a line in a coordinate system is a measure of how steep the line is. It is calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where m is the slope of the line and (x1, y1) and (x2, y2) are two points on the line.

Q: How do you graph a line in a coordinate system?

A: To graph a line in a coordinate system, you can use the following steps:

  1. Find the slope of the line.
  2. Find the y-intercept of the line.
  3. Use the slope and y-intercept to plot two points on the line.
  4. Draw a line through the two points.

Q: What is the equation of a circle in a coordinate system?

A: The equation of a circle in a coordinate system is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius of the circle.

Q: How do you find the equation of a circle in a coordinate system?

A: To find the equation of a circle in a coordinate system, you can use the following steps:

  1. Find the center of the circle.
  2. Find the radius of the circle.
  3. Use the center and radius to write the equation of the circle.

Q: What is the equation of a parabola in a coordinate system?

A: The equation of a parabola in a coordinate system is:

y = ax² + bx + c

where a, b, and c are constants.

Q: How do you find the equation of a parabola in a coordinate system?

A: To find the equation of a parabola in a coordinate system, you can use the following steps:

  1. Find the vertex of the parabola.
  2. Find the axis of symmetry of the parabola.
  3. Use the vertex and axis of symmetry to write the equation of the parabola.

Conclusion

In conclusion, the coordinate system is a fundamental concept used to represent points and locations in a two-dimensional or three-dimensional space. Understanding the properties and applications of points on the y-axis is essential for solving problems in mathematics, science, and engineering. The Q&A section provides a comprehensive guide to the coordinate system and points on the y-axis, covering topics such as the origin, x-axis, y-axis, distance formula, midpoint, slope, graphing lines, equation of a circle, and equation of a parabola.

Frequently Asked Questions

Q: What is the origin in a coordinate system?

A: The origin is the point where the x-axis and y-axis intersect. It is represented by the coordinates (0, 0).

Q: What is the difference between the x-axis and y-axis?

A: The x-axis is an imaginary line that extends infinitely in both directions and is used to measure the horizontal distance of a point from the origin. The y-axis is an imaginary line that extends infinitely in both directions and is used to measure the vertical distance of a point from the origin.

Q: What is the coordinate notation for a point on the x-axis?

A: The coordinate notation for a point on the x-axis is (x, 0), where x is the value of the x-coordinate.

Q: What is the coordinate notation for a point on the y-axis?

A: The coordinate notation for a point on the y-axis is (0, y), where y is the value of the y-coordinate.

References