`X` and `Y` Axes
- What are the `X`-and `Y`-axes?
- What is an `X`-axis?
- What is the `Y`-axis?
- Coordinate system (`X` and `Y`-axes combined)
- Locating points on the `X`-`Y` plane
- Plotting a line on the `X`- `Y` plane
- Examples
- Practice Problems
- Frequently asked questions
What are the `X`-and `Y`-axes?
`X` and `Y`-axes are the fundamental coordinate measurement systems in mathematics that are used in Coordinate Geometry to locate points on a graph and also to visualize the numbers and variables in order to understand their relationship between them.
What is an `X`-axis?
The `X`-axis is a horizontal line with marked integers. The `x`-axis is also called the horizontal axis. It represents the position of a point or object horizontally in the graph. The integers on the `x`-axis increase when we move from left to right on the axis. It is shown below. As we move from left to right, we add `1` to the previous number.
The point `0` on the axis is called the origin. You can observe that positive values are to the right of the origin and negative values are to the left of the origin.
What is the `Y`-axis?
The `Y`-axis is the perpendicular line to the `X`-axis with marked integers. The `X` and `Y`-axes intersect at the origin. So, the `Y`-axis is the vertical line, so it is also called the “vertical axis”. It is used to represent the vertical position of any point or object on the graph. The `Y`-axis is shown below.
You can observe that when you move from bottom to top, the integers get incremented by `1`. Here also, point `0` is the origin. Observe that the positive values are above the origin and the negative values are below the origin.
Coordinate system (`X` and -`Y`axes combined)
When we superimpose the `X` and `Y`-axes described above, we get the coordinate system. Specifically, it is called the Cartesian coordinate system. So, what is a Cartesian coordinate system? Let us examine the figure below.
Here you can see that after superimposing `X` and `Y`-axes, it becomes the `X`-`Y` plane, and the origin coincides with marking `(0, 0)`. Marking `(0, 0)` is the standard practice for locating any point in the `X`-`Y` plane. This system of locating any point on the `X`-`Y` plane is called the Cartesian Coordinate system.
Locating points on the `X`-`Y` plane
Let us try to locate a point `(3, 0)` on the `X`- `Y` plane. Following are the steps for locating point `(3, 0)`.
Step `1`: First, locate `3` on the `x`-axis by moving rightward from the origin.
Step `2`: Then, starting from `3` on the `x`-axis, locate `0` by moving upwards from point `3`.
Step `3`: Stop at this point and mark the point as `(3, 0)`.
You can observe that `0` is on the `x`-axis only.
So, the location of point `(3,0)` is on the `x`-axis only, as shown in the figure.
Example `2`: Locate point `P(5, 6)` on the graph.
Following the below steps.
Step `1`: Find `5` on the `x`-axis by moving rightwards from the origin as `5` is a positive integer and then stopping at `5`.
Step `2`: Move upwards from `5` to stop at `6` as `6` is also a positive integer.
Step `3`: Mark the point as `P(5, 6)`.
Plotting a line on the `X`-`Y` plane
We can also plot a line on the `X`-`Y` plane. For this to be understood, consider a line. How many points does a line have?
“Infinite”
Yes, A line has infinite points.
How many minimum points are required to draw a line?
“Two”. Yes, a line requires a minimum of two points to be drawn.
Now that we have understood this, let us try to draw a line on the graph with the given equation.
Suppose the equation `x+y=3` is a line. We can determine the points of this line. Let's see how we can do that.
For this, make a table as shown below with headers `x, y,` and points. Now put the values of `x` randomly to get values of `y` in the equation `x+y=3`.
For example, by putting `x=0` in the equation, we get the value of `y=3`. So, the resulting point is `A (0, 3)`. Similarly, we can find out the other points.
Note: Try to put feasible values as shown in the table below.
Now locate the point as described above. The points we have are `A (0, 3), B (1, 2),` and `C (2, 1)`, as shown in the figure below. Jon the points `A` and `B` to get the line `AB`. Also, you can locate point `C (2,1)` on the line `AB`. Work out the other points by putting the values in the equation `x+y=3`.
Examples
Example `1`: Plot your school location if your school’s location is `10` miles east and `20` miles north from your home. Take your home location as the origin.
Solution: To solve this problem, consider east as the `x`-axis and north as the `y`-axis. We have `10` miles in the east i.e., `10` along the `x`-axis, and `20` miles in the north direction i.e., `20` along the `y`-axis. Take your home at the origin of the `X`-`Y` graph. Plot the point as shown in the figure below to get the location of your school.
Example `2`: Plot the point `(4,5)` on a cartesian plane.
Start from the origin and move `4` units right along the `X`-axis, then move `5` units upwards along the `Y`-axis. The point is shown in the figure below.
Practice Problems
Q`1`. Choose the coordinate from the below options if the point is `5` units right of the origin and `4` units below the origin.
- `(4,5)`
- `(-4,5)`
- `(-5,4)`
- `(5,-4)`
Solution: d
Q`2`. What is an origin?
- A point on the `X`-axis
- A point on the intersection of `X` and `Y`-axes
- A point on the `X`-`Y` plane
- A point on the `Y`-axis
Solution: b
Q`3`. What are the other names of `X` and `Y` coordinates?
- Vertical point
- Horizontal point
- Abscissa and ordinate
- Origin
Solution: c
Q`4`. A line is defined by the expression `2x+y=6`? What could be one of the points lying on the line?
- `(0,3)`
- `(1,4)`
- `(3,2)`
- `(2,1)`
Solution: b
Frequently asked questions
Q`1`. What is the importance of learning the `X` and `Y`axes?
`X` and `Y`-axes are very important to learn because they have numerous applications, ranging from basic geometric location estimation to global position systems, stock market analysis, etc.
Q`2`. What is the meaning of cartesian?
The Cartesian coordinate system was developed by French mathematician René Descartes. In honor of his name, the system he developed by observing the location of flies on his ceiling, the `X`-`Y` plane system, is the Cartesian coordinate System.
Q`3`. What are quadrants in `X`- `Y`planes?
The quadrants are represented by the figure below, with their meaning described briefly.
Quadrant I: Both `X` and `Y` axes have positive integers
Quadrant II: `X`-axis has negative integers and `Y` has positive integers
Quadrant III: Both `X` and `Y` axes have negative integers
Quadrant IV: `X`-axis has positive integers and `Y` axis has negative integers