Coordinate System

Identifying a point in the coordinate system is done using two values, $X$ and $Y$.

In the next step, we will use the drawing below and demonstrate how a point can be characterized on a two-dimensional plane.

The two axes divide the plane into four quadrants. As you can see in the illustration, the first quadrant is the upper right part, marked with an $I$, and the rest follow in a counterclockwise sequence.

Each of the quadrants is characterized by different values of $X$ and $Y$, which are detailed below:

• Quadrant I - positive $X$ values and positive $Y$ values
• Quadrant II - negative $X$ values and positive $Y$ values
• Quadrant III - negative $X$ values and negative $Y$ values
• Quadrant IV - positive $X$ values and negative $Y$ values

Quadrants in a Coordinate System

Identifying a point in the coordinate system is done using two values, $X$ and $Y$.

In the next step, we'll use the drawing below and demonstrate how a point can be characterized in a two-dimensional plane.

In the drawing, we see the point $B$. We are interested in characterizing it. To do this, first, we'll draw two vertical lines from the point $B$ to each of the two axes, as shown in the drawing.

We see that on the horizontal $X$ axis, the point "meets" the value $5$, while on the vertical $Y$ axis, the point "meets" the value $2$.

It's common to write the values as points in parentheses, where the value of $X$ appears as the first value on the left, while the value of $Y$ appears as the second value, on the right.

Therefore, point $B$ would be written as follows:

$B (5,2)$

When the point is on one of the coordinates (for example, points $E$ and $G$ in the illustration)

Points in a Cartesian Coordinate System

Remember the following rule:

• When the point is on the $X$ axis, the $Y$ value is $0$, which means it has coordinates: $E (4,0)$
• When the point is on the $Y$ axis, the value of $X$ is $0$, which means it has coordinates: $G (0, 3)$

Look at the following coordinate system and these are the points $A, B, C, D$.

Solution: 

We will apply what we've learned and drop verticals from the points $A, C, D$ to each of the axes 

It should be noted that point $B$ is on the $X$ axis, and therefore, its $Y$ value is $0$. 

Answer: 

$A (2,2)$

$B (-1,0)$

$C (-2,3)$

$D (3,-2)$

Plot the following points on the coordinate system:

$k (0,5)$

$L (-1,5)$

$M (0,0)$

$N (-4,0)$

$P (2,4)$

Solution:

For points $L$ and $P$, you need to find the $X$ values and the $Y$ values where the intersection of these values is indeed the desired point.

The points $K$ and $N$ are located on the axes themselves, and therefore the following rule applies:

When the point is on the $X$ axis, the $Y$ value is $0$

When the point is on the $Y$ axis, the $X$ value is $0$

The point M is located at the intersection of the two axes.

Answer:

See the following drawing:

If you're interested in more information about "graphs," you can find detailed information in the following articles:

Data Collection and Organization - Statistical Research

Reading Information from Graphs

Graph

Discrete Graph

Continuous Graph

In the Tutorela blog, you will find a variety of articles with interesting explanations about mathematics