**The x-coordinate is the distance from the origin in the horizontal direction.**

The direction can either be on the right or left of the origin point. In this complete guide, we will discuss the coordinate systems, the Cartesian plane, and mainly about the x-axis, along with examples and detailed explanations.

## What Is X-coordinate?

The x-coordinate is the distance in a horizontal direction from the origin point, and it is represented as the first number in an ordered pair. For example, in the ordered pair $(-3,1)$, the number “-3” represents the x-coordinate, so the x-coordinate in mathematics is the value along the x-axis. The x coordinate is called an abscissa, and the latitude values of a dimensional plane are considered long x-axis, so x coordinate is also called latitude.

## Cartesian Plane

Before we delve deep into the topic of x-coordinate, it is first essential to understand the concepts of a Cartesian plane and its coordinates.

The Cartesian plane is a coordinate system formed by a combination of axes. When we deal only with one axis, it will be a single-dimensional Cartesian plane. When we are dealing with two axes, it will be called a two-dimensional Cartesian plane; when we are dealing with three axes, it is a three-dimensional Cartesian plane. The single-dimensional Cartesian plane can consist of either x-axis or the y-axis. In the two-dimensional Cartesian plane, the x and y-axis intersect, and similarly, in the three-dimensional Cartesian plane, the x-axis, y-axis, and z-axis planes intersect.

The coordinates are the ordered pair on a Cartesian plane. If we are dealing with a single-dimensional plane, it will only have one coordinate, but we mostly deal with a two-dimensional coordinate system. For example, a point $(3,4)$ can only be represented on a two-dimensional Cartesian plane as the number “$3$” represents the x-coordinate and the number “$4$” means the “$y$” coordinate. Similarly, if you are given a point $(4,-1,2)$ then we can only represent this point in a three-dimensional Cartesian plane. Here, “$4$” is the x-coordinate, “$-1$” is the y coordinate, and “$2$” is the z coordinate.

The x-coordinate will always be the first number in the ordered pair or coordinates. If we are given a two-dimensional system, then the x-coordinate will be the first, and the y-coordinate will be the second number. Similarly, if we are given a three-dimensional plane, then the x-coordinate will be the first, the y-coordinate the second, and the z-coordinate will be the third number.

For example, we are given the ordered pair $(-6,2)$, then the number “$-6$” is the x-coordinate. The easiest way to remember the pattern is that “$x$” comes first in alphabetic order as compared to “$y$,” and similarly, “$y$” comes first in the alphabetic order as compared to “$z$.” So if we are given $(2,5,1)$, then the number “$1$” will be the x-coordinate, the number “$5$” will be the y-coordinate, and the number “$1$” will be the z-coordinate.

**Example 1:** Find out the value of the x-coordinate in the ordered pair $(9,0)$.

__Solution:__

The value of the x-coordinate is $9$ in the given ordered pair.

**Example 2:** Find out the value of the x-coordinate in the ordered pair $(-3,3)$.

__Solution:__

The value of the x-coordinate is $-3$ in the given ordered pair.

We can see in the examples that the value of “x” in one ordered pair was positive, and in the second example, it was negative. Why is that so? And how do we plot or show such a value on a graph? A graphical representation of the x-coordinate can answer these questions. Still, before we jump into the graphical representation of the x-coordinate, it is essential to understand the concept of coordinate systems.

## X Coordinate and Coordinate Systems

It is imperative that you understand the concept of coordinate systems to grasp the concept of x-coordinate fully. Knowing the sign convention, magnitude, direction, and significance of the x-coordinate in a given coordinate system will help us solve questions related to analytical geometry.

What does x-coordinate tell us about the location of a point in a single, two-dimensional, and three-dimensional coordinate system? Let us discuss in detail the relation between coordinates and the Cartesian planes.

Early mathematics was divided into two main branches:

a) Algebra

b) Geometry

Mathematicians avoided using algebraic equations in geometry, and the geometrical figures and equations were not used in algebra. Then came the French mathematician Rene Descartes. He combined geometry and algebra and introduced us to the concept of the Cartesian plane or coordinates for the first time.

### Single Coordinate System or Number Line System

The number line system can be considered a single plane with only an x-coordinate as it is a horizontal line with infinite numbers from left to right. All the positive numbers or integers will be on the right-hand side of the line, and all the negative numbers will be on the left, as shown below.

As we discussed earlier, the x-coordinate is the distance from the origin in the horizontal direction. For example, we want to pinpoint the number 6 on the line. It is the distance from the origin point “$0$”. We can calculate the distance as

$d = x_{2}-x_{1}= 6 – 0 = 6$.

Similarly, we know that point “6” is three steps ahead of point “3”. Let us calculate the distance and verify whether our statement is correct.

$d = x_{2}-x_{1}= 6 – 3 = 3$.

We have discussed the examples on the right side of the origin. For example, if we want to measure the distance from the origin to “$-3$,” then we can measure the distance as

$d = x_{2}-x_{1}= -3 – 0 = -3$.

Similarly, the number “$-6$” is “$-3$” steps away from the number “$-3$,” and we can verify that by using the distance formula.

$d = x_{2}-x_{1}= -6 – (-3) = -6+3 = -3$.

Example 3: Represent the number $7$ on the single-plane system.

Solution:

The number $7$ can be represented as

**Example 3:** If a frog jumps from number $2$ to number 6 in a single plane system, then calculate the distance between these two numbers.

__Solution:__

The frog has jumped from number 2 to number 6, so we can find the distance by using the distance formula

$d = x_{2}-x_{1}= 6 – (2) = 4$.

So, the frog has jumped four places.

We have discussed the single-plane system now; let us the two-dimensional coordinate system. We use the coordinate system to locate the position of a point(s), and if we combine two or more points, it will give us the graph, and from the graph, we can write an algebraic equation.

### Two Coordinate System

In the two-dimensional coordinate system, the horizontal axis is called the x-axis. In contrast, the vertical axis is called the y-axis, and the origin point $(0,0)$ is denoted by “O.” A Cartesian coordinate system or Coordinate system is used to locate the position of any point. That point can then be plotted as an ordered pair $(x, y)$ that is known as Coordinates. The horizontal number line is called the x-axis, and the vertical number line is called Y-axis; the point of intersection of these two axes is known as the origin, which is denoted as “O.”

The positive side of the horizontal axis is denoted as $X$ while the negative side is denoted as $X^{‘}$. Similarly, the positive side of the vertical axis is denoted as $Y$ and the negative side is denoted as $Y^{‘}$. So this $XX^{‘}$ and $YY^{‘}$ will give us four quadrants.

1. The first quadrant consists of the region $XOY$.

2. The second quadrant consists of the region $X^{‘}OY$.

3. The third quadrant consists of the region $X^{‘}OY^{‘}$.

4. The fourth Quadrant consists of the region $XOY^{‘}$.

The graphical representation and the sign convention of all the quadrants are presented in the figure below.

We can see from the figure that $OX$ and $OY$ both lie in the first quadrant, and both are positive hence the first quadrant coordinates are (+,+). $OX^{‘}$ and $OY$ lie in the second quadrant and we can see that $OX^{‘}$ is negative while $OY$ is positive; hence coordinates of the second quadrant are (-,+).

Similarly, the $OX^{‘}$ and $OY^{‘}$ both lie in the third quadrant, and both are negative, so the sign convention of coordinates of the third quadrant are (-,-), and finally, $OX$ and $OY^{‘}$ lie in the fourth quadrant and as $OX$ is positive and $OY^{‘}$ is negative hence the sign convention of the coordinates of the fourth quadrant is (+,-).

- First quadrant (+,+)
- Second quadrant (-,+)
- Third quadrant (-,-)
- Fourth quadrant (+,-)

**Example 4:** The x-coordinate lies in which quadrant for the ordered pair $(5,2)$?

__Solution:__

The x-coordinate lies in the first quadrant as the sign of x-coordinate and y-coordinate is positive.

**Example 5:** The x-coordinate lies in which quadrant for the ordered pair $(-1,4)$?

__Solution:__

The x-coordinate lies in the second quadrant as the value of the x-coordinate is negative while the value of the y-coordinate is positive.

**Example 6:** The x-coordinate lies in which quadrant for the ordered pair $(2,-2)$?

__Solution:__

The x-coordinate lies in the fourth quadrant as the value of the x-coordinate is positive while the value of the y-coordinate is negative.

**Example 7:** The value of the x-coordinate lies in which quadrant for the ordered pair $(-1,-4)$?

__Solution:__

The value of the x-coordinate lies in the third quadrant as the value of the x-coordinate is negative while the value of the y-coordinate is negative too.

### Three Coordinate System

We can extend the two coordinate systems to the three coordinate systems by having an additional coordinate as “$z$.”

When the extended version of the two-dimensional coordinate system is used, it becomes possible to locate a point with three coordinates within a three-dimensional plane. In the Rene Descartes two coordinate system, it was possible to locate any object on the ground by comparing its distance from a front and side block. Notice we have mentioned that the object was placed on the ground. What if the object is in the midair and you want to locate it?

To locate the object in midair, you need the three coordinate systems as the two coordinate systems are insufficient in this scenario. In the three coordinate systems, we can locate any object suspended from the ceiling like a chandelier, etc.

We are discussing this in detail as x-coordinate is part of these coordinate systems. Without a proper understanding of the coordinate system, it will be impossible to fully grasp the concept of x-coordinate in all these plane or coordinate systems.

We know that the two-dimensional plane or coordinate system is formed when the x-axis and y-axis intercept each other. The point at which these two lines meet will be called the origin. In the three-dimensional plane or coordinate system, a third line is added to the system, which intercepts the existing two-axis, and all the three-line form an angle of $90^{o}$ with respect to each other, and the third axis is called the z-axis.

The x-axis in the three-dimensional plane will show the point(s) which lie either front or back of the origin. The y-axis will show you the location of the point that is either on the horizontal line or in the space from left to right of the origin. Finally, the z-axis will show you the position of a point lying vertically in front/top or below the origin.

Let us discuss a practical example regarding locating the coordinates in a three-dimensional system. Suppose a person is standing at Point A in a room and the coordinates of the point are $(5,2,0)$. As the value of all coordinates is positive or zero, the person would not be behind the origin. It shows that the person will be standing at a point that is five units in front of the origin, two units to the right, and zero units below or above the origin for the z-axis.

Now suppose previously, we only took the coordinates of the feet of the person, and now we want to locate the coordinates of the head of the person, and the head is in the space, and the coordinates are $(5,2,4)$.

It shows that the person’s head will be five units in front of the origin, two units to the right of the origin, and four units on the top of the origin.

**Example 8:** Find out the value of the x-coordinate in the ordered triplet $(4,0,5)$.

__Solution:__

The value of the x-coordinate is $4$ in the given ordered triplet.

**Example 9:** Find out the value of the x-coordinate in the ordered triplet $(-3,1,6)$.

__Solution:__

The value of the x-coordinate is $-3$ in the given ordered triplet.

**Example 10:** Find out the value of the x-coordinate in the ordered triplets $(4,1,-6)$.

__Solution:__

The value of the x-coordinate is $4$ in the given ordered triplet.

We have only discussed the point location method with respect to coordinates so far but these coordinates are also used in multivariate calculus and simple calculus and in the field of vector analysis. When dealing with single-variable calculus, we only deal with functions having one independent variable, “$x$.” Such functions are mostly written in the form $y = f(x)$ and the graph of such functions is represented by the points $(x,y) = (x,f(x))$.

#### Euclidean Plane

The equation $(x,y) = (x,f(x))$ shows that the following points are in the Euclidean plane, and these points in the coordinate system and two dimensional plane are represented as the ordered pair $(x,y)$ or $(a,b)$. The Euclidean plane is the plane where the geometrical rules of Euclidean are held.

Whenever the term Euclidean plane is used, it simply means we are taking some axioms, and all theorems are based on those axioms but when we are dealing with a Cartesian plane, then we are giving the axioms along with the representation of the points on the plane.

When the Euclidean space or plane is two-dimensional, then we denote it by $R^2$. Here, $2$ represents the dimension of the Euclidean plane. It has two perpendicular rays which bisect each other at an angle of $90^{o}$ and are called the x-axis and y-axis.

In multivariate calculus, vector calculus, or geometry, we deal with problems with two or more variables. The equation of the function having two variables is represented as $z = f(x,y)$, that lies the Euclidean space, which when put in the Cartesian plane will be represented as the order of three real numbers $(x,y,z)$ or $(a,b,c)$ and this dimension of Euclidean plane is represented as $R^3$.

The graph of a function having order pair as $(x,y,z)$ can be represented as $(x,y,z) = (x,y,f(x,y))$. We can represent this three-dimensional system on any flat surface, like a page or a whiteboard. In this plane, three rays are mutually perpendicular to each other, and we have xy plane, xz plane, and yz plane.

This three-dimensional Euclidean system is also called the right-handed coordinate system, as it can be represented by using the right hand, as shown in the figure below.

The thumb is upward, showing you the direction of the z-axis, the middle finger shows the direction of the y-axis, and the index finger indicates the direction of the x-axis.

The right-hand method can also be represented by pointing the thumb upwards toward the positive z-axis while we can use the remaining four fingers to rotate them from the x-axis towards the y-axis.

Using the left hand, an alternative way of representing the three-dimensional Euclidean space can also be made. Just like the right-hand rule, the thumb will point upwards representing the z-axis, while we switch the x and y-axis in the right-hand rule, and it will give us the left-hand Cartesian system, but this method is seldom used.

We have discussed the single, double, and three-dimensional Cartesian plane. What about the four-dimensional and above system? Well, as this is advanced level mathematics and it is hardly used in real-life applications, it is only used as an abstract idea. But if you are interested, you can study the work of Ludwig Schläfli and Abbot.

### Types of Coordinate Systems

There are different types of coordinate systems, but we are interested in the systems in which we deal with the x-coordinate. So let us see different types of coordinate systems and see which of those are related to the x-coordinate.

The most common coordinate system which is used in mathematics are:

- Number line
- Cartesian coordinate system
- Polar coordinate system
- Cylindrical and Spherical coordinate system

**Number Line:** As discussed earlier, this system is only represented as a single horizontal line, and yes it represents the x-coordinate system. We can say that the number line itself is a complete x-coordinate as it only means a single coordinate system.

**Cartesian Coordinate System:** As discussed earlier, this system is a two-dimensional coordinate plane consisting of the x and y-axis. So it is a two-coordinate system with x and y coordinates.

**Polar Coordinate System:** The polar coordinate system is also a two-coordinate system, but in this system, the coordinates $(x,y)$ are represented as $(r,\theta)$. The first coordinate, “r,” is also called radical coordinate, while the second coordinate $\theta$ is called angular coordinate. Note that $r$ and $\theta$ are calculated using both $x$ and $y$ so there is no concept of a separate $x$-coordinate in polar coordinate system.

Let us assume a point A in a two-dimensional coordinate plane having coordinates $(x,y)$. If we join this point to the origin, we will get a line segment. Suppose the length of the line is represented as “$r$.” The line will form an angle with the x-axis, which we call “$\theta$”.

This correspondence between the $(x,y)$ and $r$, $\theta$ is the basis of the polar coordinate system at any point of the line. We will have a value of r and “$\theta$” just like we will have a value of “$x$” and “$y$.”

Now if we use the rule of trigonometry, we can write that:

$Cos\theta = \dfrac{x}{r}$, $x = rcos\theta$

$Sin\theta = \dfrac{y}{x}$, $y = rsin\theta$

Then we know that:

$r = \sqrt{x^{2}+y^{2}}$

and:

$Tan\theta = \dfrac{y}{x}$

**Example 11:** Convert the given coordinates $(4,3)$ into polar coordinates.

__Solution:__

We can convert the given coordinates into polar form by using the formulas we have discussed. First of all, we will find the value of $r$.

$r = \sqrt{x^{2}+y^{2}} = \sqrt{4^{2}+ 3^{2}}= \sqrt{16 + 9}= \sqrt{25}= 5$

$\theta = tan^{-1}\dfrac{y}{x}= tan^{-1}\dfrac{3}{4}= 38.87^{o}$

Hence, the polar coordinates can be written as $(5, 38.87^{o})$.

**Example 12:** Convert the given polar coordinates $(5,\dfrac{\pi}{2})$ into rectangular coordinates.

__Solution:__

We can convert the given coordinates into rectangular form by using the formulas given below.

$x = rcos(\theta)$

$y = rsin(\theta)$

$x = 5 \times cos(\dfrac{\pi}{2}) = 0$

$y = 5 \times sin(\dfrac{\pi}{2}) = 5$

So the coordinates are $(0,5)$.

**Spherical Coordinate System:** The spherical coordinate system is a three dimensional coordinate system and it is mostly used to determine the surface area of an object. In this three dimensional space we deal with three coordinates $(r, \theta, \phi)$. Here, “$r$” is the radical distance, “$\theta$” is the polar angle or angular coordinate, and “$\phi$” is the azimuth angle. We use the three coordinates of Cartesian plane $(x,y,z)$ to determine these coordinates of the spherical system.

So in the spherical coordinate system, we represent any point with $(r, \theta, \phi)$.

The formulas for calculation of spherical coordinates are given below.

$Cos\theta = \dfrac{x}{r}$, $x = rcos\theta$

$Cos\phi = \dfrac{x}{r\times sin\theta}$

$r = \sqrt{x^{2}+y^{2}+z^{2}}$

### Graphical Representation

The graphing of coordinates is relatively easy, and if you have understood the concept of Cartesian planes, then the graphing of coordinates becomes even easier. As we discussed earlier, in the two and three-dimensional planes, you are also provided with other coordinates, and the graphing of the x-coordinate is done along with the other coordinates. In this section, we will show how we can draw graphs by using coordinates and how we can identify which one is the x-coordinate.

Let us assume that the value of y-coordinate remains constant, and we change the value of x-coordinate and then join the obtained points to see what sort of line we get. Suppose we keep the value of the y-coordinate as “$5$” and increase the value of the x-coordinate from $0$ to $7$. You can see from the figure below that if we join these points, we get a straight horizontal line.

So we can conclude that if the value of the y-coordinate is kept constant and we change the value of the x-coordinate, whether negative or positive, the result will always be a horizontal line.

Now let us assume that the value of the x-coordinate remains constant and we change the value of the y-coordinate and then join the obtained points to see what sort of line we get. Suppose we keep the value of the x-coordinate as “$4$” and decrease the value of the y-coordinate from $2$ to $-2$. You can see from the figure below that if we join these points, we get a straight vertical line.

So we can conclude that if the value of the x-coordinate is kept constant and we change the value of the y-coordinate, whether it is negative or positive, the result will always be a vertical line.

For our last case, suppose that we have random x and y coordinate values. We are given three points $(2,3)$, $(4,4)$ and $(5,6)$.

When we join these points, we will see that it is not always the case that we will get a straight line by joining different points. We can also form a non-linear equation by using the coordinates; any line that is not straight is a non-linear function.

Suppose we are given a function $y = x^{2}+1$; any function having a degree greater than 1 is considered a non-linear function. Here, x is an independent variable while y is the dependent variable, so the value of y will be dependent on the values of x. All the values of x will be the values of x-coordinate in the two-dimensional plane. Suppose we put a constraint in the given function and limit the value of x such that $-2\leq x \leq 2$. You can see the graph of the function given below.

We can see that when we have the limits, the value of the x-coordinate will vary from $-2$ to $2$, and on the other hand, the value of y coordinate will depend upon the value of x. We will put the corresponding value of x in the given equation and solve for y. We can see from the graph if the value of “$x$” is $-2$ or $2$, then the value of $y$ is $5$, and if the value of $x$ is $0$, then the value of $y$ is $1$. By putting the limits on x, we have automatically put the limits on the value of y. In the language of a function, all these values of x are called the domain of the function, while the values of y are called the range of the function.

So the value of the x-coordinate plays an essential role in defining the shape of the graph, and its value along with the y-coordinate can also help us determine the type of function we are dealing with.

### X-coordinate and Its Applications

The x-coordinate can be used in various mathematical applications. It would help if you keep in mind that x-coordinate alone cannot be used in any of the given applications; it is used along with other coordinates, but one cannot deny the existence of x-coordinate as it is an essential part of many critical applications in mathematics. We will cover some of the applications and try to focus on the role of x-coordinate in given applications. Some of the essential applications where coordinates are used are given below.

- Finding the distance between two points
- Finding the slope of a line
- Finding the midpoint of a line
- Writing the equation of a line
- Transformation and reflection of a function or shape
- Identifying parallel and perpendicular lines

**Distance Between Two Points:** We have already discussed the single line number system, and we know it tells us about the distance of a point in terms of the x-coordinate only from the origin point. But what if we want to measure the distance between two points in a two-dimensional plane? In this scenario, we will use both x and y coordinate values to determine the distance between two points.

Suppose we are given two points $(3,1)$ and $(6,3)$ and we want measure the distance between these two points, then we will use the formula given below.

$d =\sqrt{(x_2 – x_1)^{2}+ (y_2 – y_1)^{2}}$

$d = \sqrt{(6 – 3)^{2}+ (3 – 1)^{2}}$

$d = \sqrt{(3)^{2}+ (2)^{2}}$

$d = \sqrt{9+4}$

$d = \sqrt{13} = 3.60$

To calculate the distance between two points, you must know the value of the x coordinate and the y-coordinate.

**The Slope of the Line:** The value of the x-coordinate plays an essential role in determining the slope of a line. For example, if we consider a point $(a,0)$, “a” can be any real number. For such a number, as already discussed, we will only have a horizontal line as the value of the y coordinate will always be zero while the x-coordinate can have any value. The formula for the slope of the line is given as:

Slope $= \dfrac{y_2 – y_1}{x_2 – x_1}$

Suppose we have two points $(3,0)$ and $(4,0)$ now. Let us calculate the slope.

Slope $= \dfrac{0 – 0}{4 – 3} = 0$

So the slope of the horizontal line will always be zero; in other words, if the value of the y-coordinate is fixed at 0 and no matter what the x-coordinate is, the slope of the line will be zero.

If the value of the x-coordinate is kept constant as zero and the value of y coordinate can be any real number:

Slope $= \dfrac{y_2 – y_1}{0 – 0} = \infty$

The line having x-coordinate as zero will be vertical, and its slope will always be infinity.

Now let us calculate slope of a line with points $(4,2)$ and $(5,3)$.

Slope $= \dfrac{3 – 2}{5 – 4} = 1$

The slope of the given line is “$1$”. So we can see that the value of the x-coordinate plays an essential role in calculating the slope of a line.

**Mid-point of the Line:** We can calculate the mid-point of the line by using the x and y coordinates. Suppose we are given two points, $(6,2)$ and $(8,6)$, and we want to calculate the mid-point of the line formed by these two points. The formula for calculation of the mid-point of the line is given as:

M $= (\dfrac{x_1+ x_2}{2}, \dfrac{y_1+ y_2}{2})$

M $= (\dfrac{6 + 8}{2}, \dfrac{2 + 6}{2})$

M $= (\dfrac{14}{2}, \dfrac{8}{2})$

M $= (7,4)$

So the mid points of the line are $(7,4)$.

**Equation of a Line:** We can use the value of the x coordinate and the y coordinate to determine the equation of a line. The only condition in this scenario is that we must have more than one point available to determine the equation of the line. Suppose we are given a line having points $(4,2) $,$(8, 0)$ and $(10,-2)$. Let us see how we can calculate the equation of a line using coordinates.

First of all we will calculate the slope of the line:

$m = \dfrac{y_2 – y_1}{x_2 – x_1}$

As we are given three points, we can take any two points to calculate the slope:

Let us take $x_1 = 8$, $x_2 = 10$, $y_1 = 0$ and $y_2 = -2$

$m = \dfrac{-2 – 0}{10 – 8}= -1$

We know the equation for the line is given as $y = mx + b$. Putting value of “m” in this equation:

$y = -x + b$

We can put value of x and y coordinate for any point and determine the value of “b”

$4 = -2 + b$

$4 = -2 + b$

$b = 6$

so the final equation is $y = -x + 6$.

**Reflection of a Function:** We can perform the reflection of a function by just changing the sign of the coordinates of the function. We can also perform other transformations apart from reflection, but we will focus on the reflection function only.

We can reflect the function across the x-axis and y-axis. If we want to reflect the function across the x-axis, the sign of all the x-coordinates will remain the same while we will change the sign of the y-coordinates, which is represented as $y = -f(x)$. For example, the function y = 3x+2 reflection across x-axis will be written as $y = -3x-2$.

If we want to reflect the function across the y-axis, the sign of all the y-coordinates will remain the same while we will change the x-coordinates, which is represented as $y = f(-x)$. For example, the function $y = 3x+2$ reflection across x-axis will be written as $y = 3(-x+2)$.

**Identification of a Line:** We can identify whether a line is parallel or perpendicular to the x-axis by using the values of the coordinates. If the value of the x-coordinates is always zero or remains constant, then the line is perpendicular to x-axis. Conversely, if the value of the y-coordinates is zero and the x-coordinate has any real numbered value, then the line will be parallel to the x-axis.

**Practice Questions:**

1. Find the value of the x-coordinate in the ordered pair $(-5,1)$.

2. Find the value of the x-coordinate in the ordered pair $(-3,5)$.

3. The x-coordinate lies in which quadrant for the ordered pair $(-5,-1)$.

4. The x-coordinate lies in which quadrant for the ordered pair $(-2,1)$.

5. The x-coordinate lies in which quadrant for the ordered pair $(5,-2)$.

6. The value of x-coordinate lies in which quadrant for the ordered pair $(1,1)$.

7. Find the value of the x-coordinate in the ordered triplet $(6,0,3)$.

8. Find out the value of the x-coordinate in the ordered triplets $(-5,2,4)$.

9. Find out the value of the x-coordinate in the ordered triplets $(0,1,2)$.

10. What will be the values of x-coordinates for the points $(-6,0)$, $(8,4)$, and $(3,-3)$ when they are reflected across the x-axis.

11. What will be the values of x-coordinates for the points $(-3,1)$, $(4,0)$, and $(6,-3)$ when they are reflected across the y-axis

12. What kind of line would you get by graphing points $(3,0)$, $(6,0)$, and $(8,0)$?

13. What kind of line would you get if join the points $(0,4)$, $(0,5)$and $(0,6)$ ?

14. Is the x coordinate horizontal or vertical?

15 . What are x coordinate and y-coordinate called?

__Answer Key:__

1)

The value of the x-coordinate is $-5$ in the given ordered pair.

2)

The value of the x-coordinate is $-3$ in the given ordered pair.

3)

The x-coordinate lies in the third quadrant as the sign of x-coordinate and y-coordinate is negative.

4)

The x-coordinate lies in the second quadrant as the value of the x-coordinate is negative while the value of the y-coordinate is positive.

5)

The x-coordinate lies in the fourth quadrant as the value of the x-coordinate is positive while the value of the y-coordinate is negative.

6)

The value of the x-coordinate lies in the first quadrant as the value of the x-coordinate as well as the y-coordinate is positive.

7)

The value of the x-coordinate is $6$ in the given ordered triplet.

8).

The value of the x-coordinate is $-5$ in the given ordered triplet.

9)

The value of the x-coordinate is $0$ in the given ordered triplet.

10)

The signs of all the x-coordinates would remain the same when we reflect the points across the x-axis. The coordinates values will be $(-6,0)$, $(8,-4)$ and $(3,3)$. So we can see that the signs of x-coordinates remain the same while the signs of y-coordinates have changed.

11)

The signs of all the x-coordinates would reverse when we reflect the points across the y-axis, while the signs of y-coordinates would remain the same. So the points after reflection will be written as $(3,1)$, $(-4,0)$ and $(-6,-3)$.

12)

The y-coordinate of all the points is zero; hence the line will be a horizontal line.

13)

The x-coordinate of all the points is zero; hence the line will be a perpendicular line.

14)

The x-coordinate is horizontal.

15)

The x-coordinate is called abscissa, and the y-coordinate is called ordinate.