NCERT Solutions for Class 9 Maths Exercise 3.2 Question 1
Understanding the Question 🧐
This question asks us to recall the basic terminology used in coordinate geometry. We need to identify the names of the key components of the Cartesian plane. The Cartesian plane is a two-dimensional system that helps us locate points. This set of ncert solutions will guide you through the fundamental definitions.
Write the answer to each of the following questions:
(i) What is the name of the horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Part (i): Naming the Horizontal and Vertical Lines 📝
To locate a point on a plane, we use two perpendicular lines. These lines are the foundation of our coordinate system.
- The name of the horizontal line is the &&x&&-axis.
- The name of the vertical line is the &&y&&-axis.
Together, these two lines are called the coordinate axes.
Part (ii): Naming the Parts of the Plane 📝
When the &&x&&-axis and &&y&&-axis intersect, they divide the entire plane into four distinct regions.
- The name of each part of the plane formed by these two lines is a Quadrant.
There are four quadrants, usually numbered I, II, III, and IV, starting from the top-right and moving in an anti-clockwise direction.
Part (iii): Naming the Intersection Point 📝
The two coordinate axes meet at a single, specific point. This point is the reference for all measurements in the Cartesian plane.
- The name of the point where the &&x&&-axis and the &&y&&-axis intersect is the Origin.
The coordinates of the origin are always &&(0, 0)&&, because it is the starting point on both axes.
Conclusion and Key Points ✅
This question covers the fundamental vocabulary of coordinate geometry. We learned that the horizontal line is the &&x&&-axis, the vertical line is the &&y&&-axis, the point of their intersection is the Origin &&(0, 0)&&, and the four regions they create are called Quadrants. Mastering these terms is crucial for understanding how to plot and read points on a graph.
- ‘X‘ is a ‘cross’, so the &&x&&-axis goes across (horizontally).
- ‘Y to the sky‘, so the &&y&&-axis goes up (vertically).
- The system used to locate points on a plane is called the Cartesian coordinate system.
- The &&x&&-axis is the horizontal number line.
- The &&y&&-axis is the vertical number line.
- The intersection point of the axes is the Origin, with coordinates &&(0, 0)&&.
- The axes divide the plane into four Quadrants.
FAQ
Q: What is the name of the horizontal line in the Cartesian plane?
A: The horizontal line in the Cartesian plane is called the &&x&&-axis.
Q: What is the name of the vertical line in the Cartesian plane?
A: The vertical line in the Cartesian plane is called the &&y&&-axis.
Q: What is the point where the x-axis and y-axis intersect called?
A: The point where the &&x&&-axis and &&y&&-axis intersect is called the origin. Its coordinates are &&(0, 0)&&.
Q: How many quadrants are there in a Cartesian plane?
A: The &&x&&-axis and &&y&&-axis divide the Cartesian plane into four parts, each called a quadrant. So, there are four quadrants.
Q: What is another name for the coordinate axes?
A: The &&x&&-axis and &&y&&-axis together are known as the coordinate axes.
Q: What is the Cartesian system used for?
A: The Cartesian coordinate system is used to uniquely determine the position of a point on a plane using two numbers, called coordinates (the &&x&&-coordinate and the &&y&&-coordinate).
Further Reading
For more information on Coordinate Geometry, you can refer to the official NCERT textbook or visit the NCERT website.
