In this chapter we will learn to plot points on x-y plane with a systematic process.

Before plotting the point, let us first review the basics of cartesian pairs and ordered pairs.

## What is Cartesian Plane ?

The cartesian plane is made of horizontal x axis and vertical y axis.

X axis on right of origin has positive numbers.

X axis on left of origin has negative numbers.

Y axis above the origin has positive numbers.

Y axis below origin has negative numbers.

## What is Ordered Pair ?

Ordered Pair tells the location of a given point in cartesian plane.

Ordered Pair is represented by ( x, y ).

Where;

x ⟹ horizontal distance from origin

y ⟹ vertical distance from origin

## Plotting Points on graph using ordered pair

Here we will discuss two methods to plot point on a graph. Select the one that suits your temperament.

**Method 01**

Suppose the point P (m, n) is given.

To plot point P in graph, follow the below steps;

(a) **Select point m on x axis** and draw **imaginary perpendicular line** to x axis.

(b) **Select point n on y axis** and **draw imaginary perpendicular line** to y axis.

(c) The **point of intersection of both lines is the location of point P (m, n)**

**Method 02**

Suppose you have to plot point (m, n) on cartesian plane.

In this method, you consider yourself as a traveler who is starting a journey to reach point P (m, n)

Follow the below steps;

(a) **Start at origin (0, 0)**

(b) **Travel to point m on x axis**.

(c) Now from point m, **take 90 degree turn and travel distance n vertically**.

At the end of the travel, you will reach point (m. n)

I hope you understood the above methods. Let us now solve some problems for practice.

## Plotting points on cartesian plane – Solved Examples

**Example 01**

Plot point P (2, 3) on graph.**Solution**

We will plot the point P (2, 3) using both the above methods.

**Method 01**

Follow the below steps;

(a) Select point 2 on x axis & draw perpendicular line.

(b) Select point 3 on y axis & draw perpendicular line.

(c) The intersection of both the perpendicular line is the point P (2, 3)

**Method 02**

Follow the below steps to plot point P (2, 3)

(a) Start from origin (0, 0)

(b) Move 2 units on x axis.

(c) Turn 90 degree above and travel 3 units vertically.

After the above three steps, you will reach point P (2, 3)

**Example 02**

Plot point M (-3, -6) on cartesian plane

**Method 01**

To plot M (-3, -6), follow the below steps.

(a) Select point -3 on x axis and draw perpendicular line.

(b) Select -6 on y axis & draw perpendicular line.

(c) Point of intersection of the two perpendicular line is the location of point M (-3, -6)

**Method 02**

Follow the below steps to plot M (-3, -6)

(a) Start from origin (0, 0)

(b) Move towards -3 on x axis.

(c) Take 90 degree turn below and travel 6 units downwards.

At the end of the above steps you will reach point M (-3, -6)

**Example 03**

Plot point P (2, -3) on cartesian plane

**Method 01**

The plot point P (2, -3), follow the below steps.

(a) Select point 2 on x axis and draw perpendicular line.

(b) Select point -3 on y axis and draw perpendicular line.

(c) The intersection of both the lines is the location of point P (2, -3)

**Method 02**

Follow the below steps;

(a) Start from origin (0, 0)

(b) Travel to point 2 on x axis.

(c) Now turn 90 degree below and move 3 units.

After the above three steps you will reach point (2, -3)

**Example 04**

Plot point P (-4, 1) in cartesian graph.

**Method 01**

To plot point P (-4, 1), follow the below steps.

(a) Select point -4 on x axis and draw perpendicular line.

(b) Select point 1 on y axis & draw perpendicular line.

(c) The intersection of perpendicular lines is the location of point (-4, 1)

**Method 02**

Follow the below steps

(a) start from origin (0, 0)

(b) Travel to -4 on x axis

(c) Turn 90 degree upwards and travel one unit above.

After following above three steps, you will reach point (-4, 1)