Find 1.Abscissa, (4M) 2.Ordinate, 3.Distance From 4.X-axis, Distance 5.from Y-axis, In 4.which Quadrant These Points Lies. (i) S(-3,4) (iii) P(-4,4) (ii) M(-7,-8) (iv) D(3,5)class 9 Maths Chapter 4

Feb 28, 2025 by ADMIN 199 views

**Understanding Coordinate Geometry: Abscissa, Ordinate, Distance, and Quadrants**

Introduction to Coordinate Geometry

Coordinate geometry is a branch of mathematics that deals with the study of points, lines, and shapes in a two-dimensional plane using a coordinate system. The coordinate system is a way of representing points on a plane using a pair of numbers, called coordinates. In this article, we will focus on understanding the concepts of abscissa, ordinate, distance, and quadrants in coordinate geometry.

What is Abscissa?

The abscissa is the x-coordinate of a point in a coordinate plane. It represents the horizontal distance of the point from the y-axis. In other words, it is the distance of the point from the y-axis measured along the x-axis. The abscissa is denoted by the letter 'x'. For example, in the point (3, 4), the abscissa is 3.

What is Ordinate?

The ordinate is the y-coordinate of a point in a coordinate plane. It represents the vertical distance of the point from the x-axis. In other words, it is the distance of the point from the x-axis measured along the y-axis. The ordinate is denoted by the letter 'y'. For example, in the point (3, 4), the ordinate is 4.

What is Distance from X-axis?

The distance from the x-axis is the absolute value of the ordinate of a point. It represents the vertical distance of the point from the x-axis. For example, in the point (3, 4), the distance from the x-axis is 4.

What is Distance from Y-axis?

The distance from the y-axis is the absolute value of the abscissa of a point. It represents the horizontal distance of the point from the y-axis. For example, in the point (3, 4), the distance from the y-axis is 3.

In Which Quadrant do these Points Lie?

The quadrants are the four regions of a coordinate plane divided by the x-axis and the y-axis. The quadrants are labeled as I, II, III, and IV, starting from the upper right quadrant and moving counterclockwise.

Quadrant I: (+, +)
Quadrant II: (-, +)
Quadrant III: (-, -)
Quadrant IV: (+, -)

To determine in which quadrant a point lies, we need to look at the signs of its coordinates. If both coordinates are positive, the point lies in Quadrant I. If the x-coordinate is negative and the y-coordinate is positive, the point lies in Quadrant II. If both coordinates are negative, the point lies in Quadrant III. If the x-coordinate is positive and the y-coordinate is negative, the point lies in Quadrant IV.

Examples and Solutions

Let's consider the following points and determine their abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant.

Point (i) s(-3, 4)

Abscissa: -3
Ordinate: 4
Distance from x-axis: 4
Distance from y-axis: 3
Quadrant: II

Point (ii) m(-7, -8)

Abscissa: -7
Ordinate: -8
Distance from x-axis: 8
Distance from y-axis: 7
Quadrant: III

Point (iii) p(-4, 4)

Abscissa: -4
Ordinate: 4
Distance from x-axis: 4
Distance from y-axis: 4
Quadrant: II

Point (iv) d(3, 5)

Abscissa: 3
Ordinate: 5
Distance from x-axis: 5
Distance from y-axis: 3
Quadrant: I

Conclusion

In conclusion, the concepts of abscissa, ordinate, distance, and quadrants are fundamental in coordinate geometry. Understanding these concepts is essential to solve problems and visualize points, lines, and shapes in a two-dimensional plane. By following the steps outlined in this article, you can determine the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of any point in a coordinate plane.

Key Takeaways

The abscissa is the x-coordinate of a point in a coordinate plane.
The ordinate is the y-coordinate of a point in a coordinate plane.
The distance from the x-axis is the absolute value of the ordinate.
The distance from the y-axis is the absolute value of the abscissa.
The quadrants are the four regions of a coordinate plane divided by the x-axis and the y-axis.

Practice Problems

Try solving the following problems to practice your understanding of the concepts discussed in this article.

Find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of the point (2, 3).
Find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of the point (-2, -3).
Find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of the point (4, -2).
Find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of the point (-4, 2).

Solutions

Point (2, 3)
- Abscissa: 2
- Ordinate: 3
- Distance from x-axis: 3
- Distance from y-axis: 2
- Quadrant: I
Point (-2, -3)
- Abscissa: -2
- Ordinate: -3
- Distance from x-axis: 3
- Distance from y-axis: 2
- Quadrant: III
Point (4, -2)
- Abscissa: 4
- Ordinate: -2
- Distance from x-axis: 2
- Distance from y-axis: 4
- Quadrant: IV
Point (-4, 2)
- Abscissa: -4
- Ordinate: 2
- Distance from x-axis: 2
- Distance from y-axis: 4
- Quadrant: II

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions related to coordinate geometry, including abscissa, ordinate, distance, and quadrants.

Q1: What is the difference between abscissa and ordinate?

A1: The abscissa is the x-coordinate of a point in a coordinate plane, while the ordinate is the y-coordinate of a point in a coordinate plane.

Q2: How do I determine the quadrant of a point?

A2: To determine the quadrant of a point, you need to look at the signs of its coordinates. If both coordinates are positive, the point lies in Quadrant I. If the x-coordinate is negative and the y-coordinate is positive, the point lies in Quadrant II. If both coordinates are negative, the point lies in Quadrant III. If the x-coordinate is positive and the y-coordinate is negative, the point lies in Quadrant IV.

Q3: What is the distance from the x-axis?

A3: The distance from the x-axis is the absolute value of the ordinate of a point. It represents the vertical distance of the point from the x-axis.

Q4: What is the distance from the y-axis?

A4: The distance from the y-axis is the absolute value of the abscissa of a point. It represents the horizontal distance of the point from the y-axis.

Q5: How do I find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of a point?

A5: To find the abscissa, ordinate, distance from the x-axis, distance from the y-axis, and quadrant of a point, you need to follow these steps:

Identify the coordinates of the point.
Determine the abscissa (x-coordinate) and ordinate (y-coordinate) of the point.
Calculate the distance from the x-axis by taking the absolute value of the ordinate.
Calculate the distance from the y-axis by taking the absolute value of the abscissa.
Determine the quadrant of the point by looking at the signs of its coordinates.

Q6: Can you provide examples of points in different quadrants?

A6: Yes, here are some examples of points in different quadrants:

Quadrant I: (2, 3)
Quadrant II: (-2, 3)
Quadrant III: (-2, -3)
Quadrant IV: (2, -3)

Q7: How do I determine the quadrant of a point with negative coordinates?

A7: To determine the quadrant of a point with negative coordinates, you need to look at the signs of its coordinates. If both coordinates are negative, the point lies in Quadrant III. If the x-coordinate is negative and the y-coordinate is positive, the point lies in Quadrant II. If the x-coordinate is positive and the y-coordinate is negative, the point lies in Quadrant IV.

Q8: Can you provide a summary of the key concepts discussed in this article?

A8: Yes, here is a summary of the key concepts discussed in this article:

The abscissa is the x-coordinate of a point in a coordinate plane.
The ordinate is the y-coordinate of a point in a coordinate plane.
The distance from the x-axis is the absolute value of the ordinate.
The distance from the y-axis is the absolute value of the abscissa.
The quadrants are the four regions of a coordinate plane divided by the x-axis and the y-axis.