Cartesian Coordinate System
Introduction to the Cartesian Coordinate System
The Cartesian coordinate system is named after Rene Descartes. As a mathematician Descartes was credited with developing the system that still serves as the foundation for graphing some 350 years after his death. As a philosopher, he is famous for the phrase: “I think, therefore I am.” For more information on Descarte go to: http://www.maths.tcd.ie/pub/HistMath/People/Descartes/RouseBall/RB_Descartes.html
The Cartesian coordinate system is centered at the intersection of two perpendicular number lines. The vertical line is known as the Y axis and the horizontal line is known as the X axis.
The point where the two axes intersect is known as the origin. The intersection of the two axes forms a plane (flat surface). Every point on this flat surface can be located by two coordinates that indicate directions to the point from the origin. The coordinates of the origin are (0,0). The coordinates of the other point in the sketch below are (4,2).
To get to that point from the origin you must travel 4 units in the positive x-direction and 2 units in the positive y-direction. The first coordinate is the x-coordinate and the second coordinate is the y-coordinate. Since the coordinates are in order we frequently refer to them as ordered pairs. When you plot a point you use its coordinates to locate the point on the graph.
Now experiment with this interactive web page where you can plot a point and see the coordinate. How does it work?
Example 1 Plot and label each of the following points on the graph link below. A(4,-1) B(0,3) C(-4,-2) D(3,1) Please click here to view the graph to complete the exercise
Example 1 Solution: To view solution for graph please click here.
Example 2 Find the coordinates for each of the points for the graph link. Please click here to view the graph.
Solution: A(-4,0); B(0,-3); C(1,2); D(3,-2)
It is now your turn.
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