# 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.

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.