Plotting Points on a Graph

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). 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 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.

• 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 (x,y) moves the point along a vertical line. If the y-value is positive, the point moves “y-units” in an upward direction. However, if the y-value is negative, the point moves “y-units” in a downward direction.

Quadrants of a Cartesian Plane

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

Examples of How to Plot Points on a Graph and Identify its Quadrant

Example 1: Plot the 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.

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 (4,2).

From where I left off, I need to move two 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).

The final answer should look like this…

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

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.

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 xy-axis, then it must be in Quadrant II.

Example 3: Plot the point (5, –3) 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 means that it is in Quadrant IV.

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.

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.

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.

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.

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.

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