Plotting a Point in the Cartesian Plane  Step by Step 
In this tutorial, I have prepared eight (8) worked out examples on how to plot a point in a Cartesian plane (named in honor of French mathematician Renè Descartes). In order to plot a point, we need to have two things: a point and a coordinate plane.
Let's briefly talk about each one.
A Point 
A point in a plane contains two components where order matters! It comes in the form (x,y) where x comes first, and y comes second.
 The xvalue tells how the point moves either to the right or left along the xaxis. This axis is the main horizontal line of the rectangular axis or Cartesian plane.
 The yvalue tells how the point moves either up or down along the yaxis. This axis is the main vertical line of the rectangular axis or Cartesian plane.

Coordinate Plane (Cartesian Plane) 
A coordinate plane is composed of two lines intersecting at a 90degreeangle (making them perpendicular lines) at the point (0,0) known as the origin.
 The xcomponent of the point moves the point along a horizontal line. If the xvalue is positive, the point moves "xunits" towards the right side. On the other hand, if the xvalue is negative, the point moves "xunits" towards the left.
 The ycomponent of the point moves the point along a vertical line. If the yvalue is positive, the point moves "yunits" in upward direction. However if the yvalue is negative, the point moves "yunits" in downward direction.

The intersection of the xaxis and yaxis results to the creation of four (4) sections or divisions of the Cartesian plane.
Quadrants of a Cartesian Plane 
 The first quadrant is located at the top right section of the plane.
 The second quadrant is located at the top left section of the plane.
 The third quadrant is located at the bottom left section of the plane.
 The fourth quadrant is located at the bottom right section of the plane.

Directions: Plot the given points, and identify their locations either their quadrants or axes.
Example 1: Plot the point and identify which quadrant or axis it is located.
I will start by placing a dot at the origin which is the intersection of x and y axes. Think of the origin as the "home" where all points come from.
Next, I will move the dot from the origin 4 units to the right since x = 4 (positive in xaxis means right side movement). Remember, xvalue is the first number in the ordered pair .
From where I left off, I need to move 2 units going up parallel to the main vertical axis since y = 2 (positive in yaxis means an upward movement). The yvalue is the second number in the ordered pair .
The final answer should look like this...
The point is located in Quadrant I. Verify it here.
Example 2: Plot the point and identify which quadrant or axis it is located.
Start by placing a dot at the origin which is known as the center of the Cartesian coordinate axis.
From the origin, since x = −5, move 5 units going left .
...followed by moving the point 4 units up because y = 4.
This is the final answer. Since the plotted point is in the top left section of the xyaxis, then it must be in Quadrant II.
Example 3: Plot the point and identify which quadrant or axis it is located.
Start from the center of the Cartesian plane.
Move 5 units to the right since x = 5.
Followed by moving 3 units down since y = −3.
The final plotted point is shown below. Being in the bottom right section of the Cartesian plane, this means that it is in Quadrant IV.
Example 4: Plot the point and identify which quadrant or axis it is located.
Place a dot at the origin (center of the xyaxis). Since x = −2, move the point 2 units to the left along the xaxis. Finally, go down 5 units parallel to the yaxis because y = −5.
See the animated solution below.
(Refresh your browser if the animation is not working.)
The plotted point is located at the bottom left section of the Cartesian plane. Thus, it is in Quadrant III.
Example 5: Plot the point and identify which quadrant or axis it is located.
I start by analyzing the given ordered pair. Since x = 0, this means that there is no movement in the xaxis. However, y = 3 implies that I need to move it 3 units in the upward direction.
The plotted point is neither in Quadrant I nor in Quadrant II. To describe its location, we say that it is found along the positive yaxis.
Example 6: Plot the point and identify which quadrant or axis it is located.
This is very similar to example 5. There will be no movement along the xaxis since x = 0. On the other hand, y = − 4 tells me that I need to move the point from the origin 4 units down.
The final point is located neither in Quadrant III nor Quadrant IV. I can claim that it is found along the negative yaxis.
Example 7: Plot the point and identify which quadrant or axis it is located.
From the origin, I will move it 3 units to the left along the xaxis since x = −3. For y = 0 , it means no ymovement will follow.
The point is located neither in Quadrant II nor Quadrant III. It is found along the negative xaxis.
Example 8: Plot the point and identify which quadrant or axis it is located.
With x = 2, I need to move it 2 units to the right. Having y = 0 implies that no ymovement will occur.
The plotted point is located neither in Quadrant I nor Quadrant IV. It is found along the positive xaxis.
