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## Ordered Pairs

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.

to see how to draw a grid:    The following example illustrates how to represent an ordered pair as a point on this grid.

### Example 1.

To plot the point represented by (2,4):

First draw a vertical line through x =2.

Next draw a horizontal line through y =4.

The point (2,4) is at the intersection of these two lines, P. 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. ### Exercise 1.

Enter the correct coordinates for the points plotted below, A-L.
Remember to separate your x and y coordinates by a comma. A: ( ) B: ( ) C: ( ) D: ( ) E: ( ) F: ( ) G: ( ) H: ( )  I: ( ) J: ( ) K: ( ) L: ( )

The two axes partition the plane into 4 regions, called quadrants.
They are referred to as the 1st, 2nd, 3rd, and 4th quadrant as shown. • If the x and y coordinates are both positive, the point is located in the 1st quadrant.
• If the x coordinate is negative and the y coordinate is positive, the point is located in the 2nd quadrant.
• If the x and y coordinates are both negative, the point is located in the 3rd quadrant.
• If the x coordinate is positive and the y coordinate is negative, the point is located in the 4th quadrant.

### Example 2.

Look at the following example to see which quadrants various points are located in. Check the grid below to confirm the solution. 