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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.

label of a point (x,y) where x comes first, and y comes second in the order

 

  • The x-value tells how the point moves either to the right or left along the x-axis. This axis is the main horizontal line of the rectangular axis or Cartesian plane.

 

  • The y-value tells how the point moves either up or down along the  y-axis. 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 90-degree-angle (making them perpendicular lines) at the point (0,0) known as the origin.

 

cartesian plane or coordinate plane showing the x and y axes

 

  • The x-component of the point (x,y) moves the point along a horizontal line. If the x-value is positive, the point moves "x-units" towards the right side. On the other hand, if the x-value is negative, the point moves "x-units" towards the left.

 

  • The y-component of the point the form of a generic point (x,y) moves the point along a vertical line. If the y-value is positive, the point moves "y-units" in upward direction. However if the y-value is negative, the point moves "y-units" in downward direction.

 

The intersection of the x-axis and y-axis results to the creation of four (4) sections or divisions of the Cartesian plane.

 

Quadrants of a Cartesian Plane

 

the quadrants of a cartesian plane: I, II, III and IV positioned counter-clockwise

 

  • 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: point (4,2) See Solution
Example 2: point (-5,4) See Solution
Example 3: point (5,-3) See Solution
Example 4: point (-2,-5) See Solution
Example 5: point (0,3) See Solution
Example 6: point (0,-4) See Solution
Example 7: point (-3,0) See Solution
Example 8: point (2,0) See Solution

 


Example 1: Plot the point point (4,2) 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.

 

showing where the point of origin in the cartesian or coordinate plane

 

Next, I will move the dot from the origin 4 units to the right since x = 4 (positive in x-axis means right side movement). Remember, x-value is the first number in the ordered pair point (4,2).

move 4 units to the right

From where I left off, I need to move 2 units going up  parallel to the main vertical axis since y = 2 (positive in y-axis means an upward movement). The y-value is the second number in the ordered pair (4,2).

 

move 2 units up the plane parallel to y-axis

The final answer should look like this...

 

showing how the point (4,2) is plotted in the xy-axis

 

The point (4,2) is located in Quadrant I. Verify it here.

 


Example 2: Plot the point (-5,4) 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.

 

shows where the point of origin is located

 

From the origin, since x = −5, move 5 units going left .

 

move 5 units to the left along the x-axis

 

...followed by moving the point 4 units up because y = 4.

 

move 4 units parallel to the y-axis

 

This is the final answer. Since the plotted point is in the top left section of the xy-axis, then it must be in Quadrant II.

shows how the point (-5,4) is plotted in the cartesian plane

 

 


Example 3: Plot the point (5,-3) and identify which quadrant or axis it is located.

 

Start from the center of the Cartesian plane.

point of origin in xy-axis

Move 5 units to the right since x = 5.

moving 5 units going to the right

Followed by moving 3 units down since y = −3.

move down 3 units

 

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.

plotting the point (5,-3)

 

 

 


Example 4: Plot the point (-2,-5) and identify which quadrant or axis it is located.

Place a dot at the origin (center of the xy-axis). Since x = −2, move the point 2 units to the left along the x-axis. Finally, go down 5 units parallel to the y-axis because y = −5.

 

See the animated solution below. see more examples

(Refresh your browser if the animation is not working.)

 

 

animated gif illustrating how to plot the point  (-2,-5)

 

 

 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 (0,3) 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 x-axis. However, y = 3 implies that I need to move it 3 units in the upward direction.

 

zero value in x-coordinate means no movement in the horizontal axis plot the point (0,3). move 3 units upward only.

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 y-axis.

 


Example 6: Plot the point (0,-4) and identify which quadrant or axis it is located.

This is very similar to example 5. There will be no movement along the x-axis since x = 0. On the other hand, y = − 4 tells me that I need to move the point from the origin 4 units down.

no movement in x-axis. -4 means move 4 units down. the plot of the point (0,-4)

The final point is located neither in Quadrant III nor Quadrant IV. I can claim that it is found along the negative y-axis.

 


Example 7: Plot the point (-3,0) and identify which quadrant or axis it is located.

From the origin, I will move it 3 units to the left along the x-axis since x = −3. For y = 0 , it means no y-movement will follow.

a zero value in y-coordinate means no movement along the y-axis plotting the point (-3,0) in the coordinate plane

 The point is located neither in Quadrant II nor Quadrant III. It is found along the negative x-axis.

 


Example 8: Plot the point (2,0) 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 y-movement will occur.

move 2 units to the right the plot of the point (2,0)

The plotted point is located neither in Quadrant I nor Quadrant IV. It is found along the positive x-axis.

 


 

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About This Topic: Plotting Points in the Cartesian Plane

 

Practice Problems with Answers
Worksheet 1 Worksheet 2

 

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