Coordinate Systems
According to the Ruler Postulate, the points on a line can be numbered so that to every point there is matched number called its coordinate.
A line numbered in this way is a one dimensional coordinate system (number line).
One Dimensional Coordinate System
![One Dimensional Coordinate System](https://www.geogebra.org/resource/wev8fdzb/wkFyMRhBiFttWFbn/material-wev8fdzb.png)
If two lines are numbered according to the Ruler Postulate are perpendicular to one another (as shown in the figure below) the number lines become the axes of a two dimensional coordinate system.
The axes are labeled x and y, and the point in which they intersect, zero on each axis, is labeled with a capital O and is the origin of the coordinate system.
The axes separate the plane that contains them into four parts (quadrants). The quadrants are identified by Roman numerals.
Roman Numeral | Counting Number |
I | 1 |
II | 2 |
III | 3 |
IV | 4 |
![The axes of a two dimensional coordinate system.](https://www.geogebra.org/resource/zfcn4kdy/VoBnmC8tvhLJbukM/material-zfcn4kdy.png)
To find the coordinates of any given point on a coordinate plane, locate the point and draw a perpendicular line from the point to the x axis. That is the point's x coordinate.
Return to the same point and draw a perpendicular line from the point to the y axis. That is the point's y coordinate.
How to find the coordinates of a point
![How to find the coordinates of a point](https://www.geogebra.org/resource/h8yq2wdq/VjqgSKmxAxY7LxoC/material-h8yq2wdq.png)
Definitions
The x-coordinate of a point is the number located on the x-axis (back and forth line)
The y-coordinate of a point is the number located on the y-axis (up and down line)
The coordinates of a point are written in parentheses and separated by a comma
The x coordinate is ALWAYS listed first (x,y)
The following exercises refer to the figure below.
![The following exercises refer to the figure below.](https://www.geogebra.org/resource/uvfjsnbx/6wdHIH8GClbeeQd7/material-uvfjsnbx.png)
Question 1
What are the lines labeled x and y called?
Question 2
What is the point labeled O called?
Question 3
Which quadrant is point P in?
Question 4
What is the x-coordinate of point P?
Question 5
What is the y-coordinate of point P?