In math, coordinate systems form the basis of a link between geometry and algebra. They are very useful for visualizing problems. The cartesian plane is one of the most used coordinate systems and forms the basis for much of skills needed in higher level math.
Pretend for a second it is 1995. GPS systems are not available to most people and you need to find your way to a friends house using a map. You are new to the area and do not know where to find the street your friend lives on. With many maps, they are labeled across the top with letters and the side with numbers. To find the street, you can look it up in an index. Let's say the index tells you the street is located in square D3. You can look at the top of the map and find the D. You then move down the map until you are inline with the 3 on the side of the map. You now know where the street is that you are trying to find.
What was just described is a coordinate system. Based on different measurements in perpendicular directions we were able to locate a single point on a map. In math coordinate systems are used as well. The most popular coordinate system is the Cartesian Plane. A plane is a flat surface of 2 dimensions. The Cartesian Plane is essential 2 number lines. The first stays horizontal and is called the x-axis. The second is turned on its side so that it is perpendicular to the x-axis. This line is called the y-axis. The point at which they meet is called the origin.
As can be seen by the image above. The number lines go on forever in both the positive and negative direction. Now that we have our system, we can begin to locate points on the plane. Points on a cartesian plane are represented by what is called an ordered pair. An ordered pair is two numbers, the first representing the x value of the location, the second representing the y-value of the location.
For example, the ordered pair (3, 4) means that to get to this location on our graph, we start at the origin (0,0). Then we go to the right 3 spaces on the x-axis, and then move up 4 spaces along the y-axis. The point (3,4) can be seen in blue.
Below is a graph showing some more points. Notice that for negative x values we move left on the graph, for negative y values we move down.
Quadrants
When the x-axis and y-axis intersect, they form 4 areas. Each of these areas is called a Quadrant. Each quadrant is typically represented by a roman numeral starting with the top right and going counter-clockwise around the origin.
- Quadrant I (one) is all points (or ordered pairs) which have a positive x and a positive y. (x,y)
- Quadrant II (two) is all points which have a negative x and a positive y. (-x, y)
- Quadrant III (three) is all points which have a negative x and a negative y. (-x,-y)
- Quadrant IV (four) is all points which have a positive x and a negative y. (x, -y)
All points lie in one of these four quadrants unless either their x value equals 0 or their y value equals 0, or both values equal 0.