Are you searching for the information regarding the Quadrants and Convention for Signs of Coordinates on various websites? If our guess is correct, then you are on the right page. Stop your search and start your preparation now. Here you can get complete and brief info about the quadrants and signs of coordinates. Know what is quadrant and what are the signs of the coordinates in each quadrant from here. Also, the students of grade 9 can find examples on the quadrants of coordinate geometry in the below sections.
Also Read:
What are the Sign Convention of the Coordinates?
What is Quadrant?
In a coordinate plane, a quadrant is defined as the region of a cartesian plane formed by the two axes i.e, x-axis and y-axis. The region of the plane falling in XOY is the first quadrant, the region of the plane falling in X’OY is the second quadrant, the region of the plane falling in X’OY’ is the third quadrant, and the region of the plane falling in XOY’ is the fourth quadrant.
Four Quadrants in a Plane:
1st Quadrant: The upper right-hand corner is the first quadrant. In this quadrant x and y values are positive.
2nd Quadrant: The upper left-hand corner is the second quadrant. In this quadrant, the value of x is negative and the value of y is positive.
3rd Quadrant: The lower left-hand corner is the third quadrant. In this quadrant both the x and y values are negative.
4th Quadrant: The fourth quarter is at the lower right-hand corner, in which the x value is positive(+) and y value is negative(-).
What are the Signs of the Coordinates in Each Quadrant?
| Quadrants | x-coordinate | y-coordinate |
| Quadrant – I | Positive (+) | Positive (+) |
| Quadrant – II | Negative (-) | Positive (+) |
| Quadrant – III | Negative (-) | Negative (-) |
| Quadrant – IV | Positive (+) | Negative (-) |
From the table, we observe that there are two signs of the coordinates in each quadrant.
Quadrant – I: In the first quadrant both the coordinates have positive signs.
Quadrant – II: In the second quadrant x-coordinate has a negative sign and the y-coordinate has a positive sign.
Quadrant – III: In the third quadrant both the coordinates have negative signs.
Quadrant – IV: In the fourth quadrant x-coordinate has a positive sign and the y-coordinate has a negative sign.
Quadrants and Convention for Signs of Coordinates Examples
Example 1.
Check and answer to which quadrants do the given points lie?
(2, 4)
(-4, -5)
(-3, 6)
(4, -4)
Solution:
The coordinates of (2, 4) are positive, thus it lies on the first quadrant.
The coordinates of the point (-4, -5) are both negative, thus it lies on the third quadrant.
The coordinates of the point (-3, 6) are negative on the x-axis and positive on the y-axis, thus it lies on the second quadrant.
The coordinates of the point (4, -4) are positive on the x-axis and negative on the y-axis, thus it lies on the fourth quadrant.
Example 2.
Give an example of a point that lies on the third quadrant.
Solution:
In the third quadrant, the coordinates of the x-axis and y-axis both are negative.
(-6, -8) is an example of a point in the third quadrant.
Example 3.
Where does the point (-6, 0) lie in the cartesian plane? Does it lie in a quadrant?
Solution:
The point (-6, 0) lies on the horizontal axis or x-axis,
which is at a distance of 6 units from the origin. It does not lie in any quadrant.
Example 4.
Give an example of a point that lies on the second quadrant.
Solution:
In the third quadrant, the coordinates of the x-axis are negative and the y-axis is positive.
(-4, 7) is an example of a point in the third quadrant.
Example 5.
Where does the point (-1,4) lie?
Solution:
Given that the point is (-1,4)
The point x coordinate is negative and the y coordinate is positive so the point lies in the second quadrant.
FAQs on Quadrants and Convention for Signs of Coordinates
1. What is a quadrant?
A quadrant is defined as the region of a cartesian plane. It is formed when the x-axis and y-axis both intersect each other.
2. What is the intersection of two axes called?
The intersection of the x-axis and y-axis is called the reference point or the origin.
3. What are the Four Quadrants in a Coordinate Plane?
The graph has been divided into 4 parts.
1st Quadrant: In a graph, the upper right-hand corner is the first quadrant. In this quadrant x and y values are positive.
2nd Quadrant: In a graph, the upper left-hand corner is the second quadrant. In this quadrant, the value of x is negative and the value of y is positive.
3rd Quadrant: In the graph, the lower left-hand corner is the third quadrant. In this quadrant both the x and y values are negative.
4th Quadrant: In the fourth quarter is at the lower right-hand corner, which the x value is positive and the y value is negative.