In this chapter we will discuss the basic concept & definition of ordered pair in geometry with solved examples.
Let us first review the basics of cartesian plane.
What is cartesian plane ?
Cartesian plane is made up two straight vertical and horizontal line.
Horizontal line is called X axis and vertical line is called Y axis.
Given below is the image of cartesian plane.
In the above image;
⟹ x axis is shown by red line.
On the right of origin, the value of x axis is positive and on left the values are negative.
⟹ y axis is shown by blue line
The values of y axis above origin is positive and the values below it are negative.
Ordered Pair definition
The location of any point in cartesian plane is shown by Ordered pairs.
The ordered pair contains two inputs, x coordinate & y coordinate, which tells the position of point in coordinate plane.
For example;
Consider the point P (-5, 6) in cartesian plane.
Ordered Pair (-5, 6) tells;
X axis position ⟹ -5
Y axis position ⟹ 6
Plotting the position of point P (-5, 6) in cartesian plane.
Example 02
consider point L (3, 4) in cartesian plane
Solution
The ordered pair (3, 4 ) tells;
X axis position ⟹ 3
Y axis position ⟹ 4
Plotting the point P in cartesian plane.
Can we interchange the digits in Ordered Plane ?
No !!
Interchanging the digits in ordered plane will result in different location.
For example;
Consider the point (2, 3)
If we interchange the digit, we get (3, 2).
Now the ordered pair (2, 3) is completely different from (3, 2)
Given below is the position of both the ordered pair in cartesian coordinate.
Note that both the ordered pair are showing different location.
Hence, we cannot use the data of ordered pair interchangeably.
Thus, \mathtt{( 2,\ 3) \ \neq \ ( 3,\ 2)}\
Locating point in cartesian plane using Ordered Pair
Given below are steps to plot point using ordered pair.
(a) Locate the distance from x & y axis using ordered pair data.
(b) Draw imaginary line perpendicular to x axis position.
(c) Similarly draw imaginary perpendicular line from y axis position.
(d) The point of intersection of both the perpendicular line is the location of given ordered pair.
Let us understand the steps with the help of examples.
Example 01
Locate point P (3, -5) on cartesian plane.
Solution
The ordered pair P (3, -5) tells;
X axis position ⟹ 3
Y axis position ⟹ -5
Let’s draw perpendicular lines from both the points.
The point of intersection of the perpendicular lines is the location of given point P ( 3, -5)
Example 02
Locate point P (-1, -2) on cartesian plane
Solution
X axis position ⟹ -1
Y axis position ⟹ -2
Draw imaginary perpendicular lines from point x = -1 & y = -2.
The point of intersection of both the lines is the location of given point P (-1, -2)
Example 03
Locate the point (-6, 4) in cartesian plane.
Solution
X axis position ⟹ -6
Y axis position ⟹ 4
Plotting imaginary perpendicular lines from the point x = -6 and y = 4.
The intersection of both the lines gives the location of point (-6, 4)
