# 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.