# 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 to 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 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).

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, this 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.

(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 **(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.