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)
