Quadrant is the region enclosed by the intersection of the X-axis and the Y-axis. On the cartesian plane when the two axes, X-axis and Y-axis, intersect with each other at 90º there are four regions formed around it, and those regions are called quadrants. So, every plane has four quadrants each bounded by half of the axes. Each quadrant is denoted by Roman numerals and named as Quadrant I, Quadrant II, Quadrant III, and Quadrant IV based on their position with respect to the axes.
|1.||What is a Quadrant?|
|2.||What are the 4 Quadrants?|
|3.||How to Plot Points on Quadrants?|
|4.||Solved Examples on Quadrants|
|5.||Practice Questions on Quadrants|
|6.||FAQs on Quadrants|
What is a Quadrant?
In the cartesian system, a plane is divided into four regions by a horizontal line called X-axis and a vertical line called Y-axis.
Quadrant Definition: A quadrant can be defined as a region/part of a cartesian plane which is obtained when the two axes intersect each other. It is used to determine the position of a point in a plane.
What are the 4 Quadrants?
The X and the Y axes divide the plane into four graph quadrants:
- The first quadrant is on the upper right-hand corner of the plane. In this quadrant, both x and y-coordinates are positive.
- The second quadrant is on the upper left-hand corner of the plane. In this quadrant, the x-coordinate is negative and the y-coordinate is positive.
- The third quadrant is on the lower left-hand corner of the plane. In this quadrant, both x and y-coordinates are negative.
- The fourth quadrant is on the lower right-hand corner of the plane. In this quadrant, the x-coordinate is positive and the y-coordinate is negative.
It should be noted that the quadrants are numbered in an anti-clockwise direction.
The point where the X-axis and the Y-axis meet is called the origin.The values of x and y at the origin are (0,0).
If we observe the horizontal axis 'x', as we move from left to right, we see that the value of the coordinates increases. Similarly, on the vertical axis 'y', as we go in the upward direction, the value goes on increasing. So, the sign convention of the four quadrants will be as shown below:
How to Plot Points on Quadrants?
The numbers in the quadrant are the ordered pair (a, b) where 'a' is the x- coordinate and 'b' is the y-coordinate. To understand how to plot a point in the four quadrants, we need to observe the signs of an x-coordinate (also called abscissa) and a y-coordinate (also called ordinate). This gives an idea about the quadrant in which the given point lies. For example, we are given a point P (-4,6). Without even plotting it on a graph, by observing its sign (-ve, +ve) we can make out that it lies in the quadrant II .
- The abscissa gives the information about the horizontal distance of the point from the Y-axis and its sign tells the direction, i.e., left or right. For example, abscissa = -4 means, starting from the origin, we need to go along the x-axis in a negative direction (left) up to 4 units.
- The ordinate gives the information about the vertical distance of the point from origin and its sign tells the direction, i.e., above or below the origin. In the above example, ordinate = 6 means, starting from the origin, we need to go along the y-axis in a positive direction (up) up to 6 units.
Let's plot the point D (5,-3) on a cartesian plane. First, observe the sign to identify its quadrant. The point is of the type (+ve, -ve) which lies in quadrant IV. Abscissa = 5; So, take a point P at a distance of 5 units from the origin on the right-hand side. Ordinate = -3; So, move the point P vertically down by a distance of 3 units.
Topics Related to Quadrants
Check out these interesting articles related to the topic quadrant.
- The origin (0,0) lies on both X and Y axes.
- X-coordinate is also called abscissa and the y-coordinate is also known as ordinate.
Try to solve these challenging questions related to Quadrants:
- A parallelogram ABCD has two of its coordinates as A (-2, 2) and B (8, 2). Find its remaining coordinates. Is your answer unique?
- In the above question, if you are given information that C lies in the IV quadrant, will you still get the same ordered pairs for C and D?
Solved Examples on Quadrant
Example 1: Ms. Cathy asks the students to write the coordinates of points A and B given in the graph and identify the quadrant in which each of them lies. Can you help Nora to get the answer to this?
Solution: Distance of A from y-axis = OP = 3 units on its left. Therefore, Abscissa = -3. Distance of A from x-axis = AP = 4 units above it. Therefore, Ordinate = 4. Similarly, Distance of B from y-axis = OM = 4 units on its right. Therefore, Abscissa = 4. Distance of B from x-axis = BM = 3 units below it. Therefore, Ordinate = -3. The answer to the above problem can be recorded in a tabular form.
Point Coordinates Quadrant A (-3, 4) II B (4, -3) IV
Example 2: Peter is required to locate the points M (3, 0), N (3,5), and P (3, -2) on a cartesian system and check if they are collinear. Help Peter to do this.
Solution: Let's plot the points M, N, and P on a graph. To know whether the three points are collinear or not, we need to draw a line passing through any two of them. If the third point also lies on that line, then the points will be collinear.
We can observe that line 'l' contains all three points. Therefore, M, N, and P are collinear points.
FAQs on Quadrant
What are the 4 Quadrants?
The x and the y axes divide the plane into four graph quadrants.These are formed by the intersection of the x and y axes and are named as: Quadrant I, II, III, and IV. In words, we call them first, second, third, and fourth quadrant. All the quadrants are different from each other based on the position and symbol of the x and y-coordinates.
Which Quadrant is Positive?
Quadrant I contains the positive values of x and y, so it is considered a positive quadrant. Other than this, quadrant II has negative x-coordinates and positive y-coordinates, quadrant III has both negative coordinates and quadrant IV contains the positive values of x but negative values of y.
What is in the Right Upper Quadrant?
The right upper quadrant is the first quadrant containing all the positive values of the x and y axes starting from 0, i.e., the origin.
Is Quadrant 4 Positive or Negative?
In quadrant 4, the x-coordinates are positive and the y-coordinates are negative.
Is Quadrant 1 Positive or Negative?
In quadrant 1, both x and y coordinates are positive. Hence, it is positive.