NCERT Class 9 Maths Solutions: Coordinate Geometry

Question:

To describe the position of an object, we need a reference point and a way to measure distance and direction from that reference point. This is the fundamental idea of position description.


To describe the position of a table lamp on your study table, you can use the following methods:

1. Using a Corner of the Table as a Reference:
* Imagine the study table as a flat surface.
* Pick one corner of the table as your starting point (origin).
* Then, describe the lamp’s position by stating its distance along two perpendicular directions from that corner. For example: “The lamp is 50 centimeters from the left edge of the table and 30 centimeters from the front edge of the table.”

2. Using the Center of the Table as a Reference:
* Alternatively, you can consider the center of the table as your reference point.
* You would then describe the lamp’s position relative to this center, possibly using distances and directions. For example: “The lamp is approximately 20 centimeters to the right of the center of the table and slightly towards the back.”

3. Using a Landmark Object as a Reference:
* If there are other objects on the table, you can use them as reference points. For example: “The lamp is placed to the right of my laptop,” or “The lamp is situated in the back corner of the table, near the bookshelf.”

In essence, you are defining a coordinate system (even if informal) and then providing the coordinates or relative location of the lamp within that system. The key is to be clear about your reference point and the directions you are using.

Question:

Coordinate geometry, specifically representing points in a 2D plane using ordered pairs (x, y). The first number represents the position along one axis (e.g., North-South direction) and the second number represents the position along the other axis (e.g., East-West direction).


The city’s street plan can be visualized as a coordinate system. The North-South roads can be considered as lines parallel to the y-axis, and the East-West roads as lines parallel to the x-axis. The question uses a convention to refer to cross-streets, which is essentially naming a point of intersection.

1. How many cross-streets can be referred to as (4, 3)?
The notation (4, 3) means the cross-street formed by the 4th street running in the North-South direction and the 3rd street running in the East-West direction. Since there is only one specific 4th street in the North-South direction and only one specific 3rd street in the East-West direction, they will intersect at exactly one point. Therefore, there is only one cross-street referred to as (4, 3).

2. How many cross-streets can be referred to as (3, 4)?
Similarly, the notation (3, 4) refers to the intersection of the 3rd street in the North-South direction and the 4th street in the East-West direction. Again, there is only one such 3rd North-South street and one such 4th East-West street. They will intersect at a single, unique point. Therefore, there is only one cross-street referred to as (3, 4).

Question:

The question is about the parts of a Cartesian plane. A Cartesian plane is formed by two perpendicular lines: the horizontal line called the x-axis and the vertical line called the y-axis. These lines intersect at the origin. The plane is divided into four regions by these axes.


The horizontal line in a Cartesian plane is called the x-axis, and the vertical line is called the y-axis. These two lines intersect at a point called the origin (0,0). Together, the x-axis and y-axis divide the plane into four regions. Each of these regions is called a quadrant. These quadrants are numbered in a counter-clockwise direction, starting from the upper-right.
Quadrant I: The region where both x and y coordinates are positive.
Quadrant II: The region where the x-coordinate is negative and the y-coordinate is positive.
Quadrant III: The region where both x and y coordinates are negative.
Quadrant IV: The region where the x-coordinate is positive and the y-coordinate is negative.

Question:

The Cartesian coordinate system is a two-dimensional plane used to locate points. It consists of two perpendicular lines: the horizontal line and the vertical line. The intersection of these lines is the origin.


The horizontal line drawn in the Cartesian plane is called the x-axis. The vertical line drawn in the Cartesian plane is called the y-axis. These two lines are perpendicular to each other and intersect at the origin (0,0), which serves as the reference point for locating any other point in the plane. The position of any point is then uniquely determined by its distance from these two axes, represented by its x-coordinate and y-coordinate, respectively.

Question:

The Cartesian coordinate system is a two-dimensional plane where points are located using two perpendicular lines: the horizontal axis (x-axis) and the vertical axis (y-axis). The point where these two axes intersect has specific coordinates.


The point where the horizontal line (x-axis) and the vertical line (y-axis) intersect is called the origin. This point is defined as the reference point for locating all other points in the coordinate system. Its coordinates are always (0, 0).