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Math: Ordered Pairs - Tutorial
The Coordinate Plane
This section will cover the fundamentals of plotting ordered pairs on a coordinate plane.
Parts of the Coordinate Plane
- The horizontal boldface line is called the x-axis.
- The vertical boldface line is called the y-axis.
- The point where the two lines intersect is called the origin.
- The x-axis and the y-axis intersect to create four quadrants.
- A quadrant is an area in the coordinate plane.
4th Quadrant
3rd Quadrant
2nd Quadrant
1st Quadrant
To plot the y-coordinate:
1. Start at the origin (0,0).
2. If the y-coordinate is positive
move above the x-axis.
3. If the y-coordinate is negative,
move below the x-axis.
Take one ordered pair at a time and plot each point in the coordinate plane. To plot these points, follow the steps below.
A
B
C
D
E
F
G
H
(-2, 4)
( 3, 0)
( 4,-1)
(-5, 2)
( 4, 3)
( 7,-5)
(-4, -4)
(-2, -6)
Move 2 spaces left of the y-axis. Then move 4 spaces above the x-axis.
Move 3 spaces right of the y-axis. Then move zero spaces from the x-axis.
Move 4 spaces right of the y-axis. Then move 1 space below the x-axis.
Move 5 spaces left of the y-axis. Then move 2 spaces above the x-axis.
Move 4 spaces right of the y-axis. Then move 3 spaces above the x-axis.
Move 7 spaces right of the y-axis. Then move 5 spaces below the x-axis.
Move 4 spaces left of the y-axis. Then move 4 spaces below the x-axis.
Move 2 spaces left of the y-axis. Then move 6 spaces below the x-axis.
Ordered Pairs
A point is plotted in the coordinate plane with the help of the x-coordinate and the y-coordinate. These two coordinates work as a team or, in this case, a pair.
The order of the pairs is the same as how the x and y occur in the letters of the alphabet. The x-coordinate comes before the y-coordinate.
The two coordinates are joined together inside parentheses and separated by a comma.
Example 1: (x, y)
Let's say you want to assign some numbers to the following two coordinates. You could choose any positive or negative whole number.
Example 2:
The ordered pairs have been assigned to points A through H.
Point A has an x-coordinate of -2 and a y-coordinate of 4.
Point B has an x-coordinate of 3 and a y-coordinate of 0, and so on.
How to Plot Points
Example:
To plot the x-coordinate:
1. Start at the origin (0,0).
2. If the x-coordinate is negative,
move to the left of the y-axis.
3. If the x-coordinate is positive,
move to the right of the y-axis.
