- 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

`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.

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.

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.

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.

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)`.

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`.

**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.

**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

**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