An ordered pair is simply a pair of elements written in a certain order (order is important). For example, the numbers 5 and 2 can form two ordered pairs:
(5,2) and (2,5).
In general, given two numbers x and y, the two ordered pairs (x,y) and (y,x) are different, unless x = y.
The number x is called the first component and y the second component of the ordered pair (x,y).
Ordered pairs have many uses. It can be used to represent an object with two distinguishable parts. For example, a complex number x+iy can be represented by the ordered pair (x,y). In an Excel spreadsheet we use a letter and a number to denote a cell on the sheet.
On a street map we use the same method to locate a street.
Cartesian Coordinate System in 2-D
Ordered pairs are useful in representing relationships between two sets of data, in the form of a graph. These can then be represented by points on a grid known as the Cartesian Coordinate System in 2-D.
The following example illustrates how to represent an ordered pair as a point on this grid.
To plot the point represented by (2,4):
More Exercises (opens in another window)
If a point P is represented by (a,b) we call a and b the coordinates of P. In 2-D Cartesian Coordinates, the first coordinate in the ordered pair is called the x-coordinate and the second coordinate in the ordered pair is called the y-coordinate.
the correct coordinates for the points plotted below, A-L.
The two axes partition the plane into 4 regions, called
Look at the following example to see which quadrants various points are located in. Check the grid below to confirm the solution.