CARTESIAN COORDINATES
Analysis
 
1. HOW THE PLANE IS ORGANISED
The French philosopher and mathematician, René Descartes (1596-1650) developed his philosophy on the idea of needing a starting point on which all other knowledge can be based: I think, therefore I am. In the world of mathematics he is the founder of analytic geometry, which uses a pair of perpendicular lines that cross at a point called the origin as its basis, and is also referred to as the Cartesian coordinates system.
1.- Put the cursor somewhere on the diagram on the left, click on the left hand button of the mouse, move the mouse and watch what happens.
 
The straight white lines that stand out are called the Axes and the point where they cross is called the Origin.

2.-In your notebook draw the rectangular coordinates system with its axes and origin.
2. THE CARTESIAN PLANE
The horizontal axis is called the X-axis, the vertical axis is called the Y-axis and the fixed point O is called the origin.
3.- Change the scale and move the axes to see how all points on the plane can be located using this system (O;X,Y).
 
Use the coloured arrows next to the zoom and the OX and OY axes.
Click on the Start button (init) to go back to the initial values.

4.-In your notebook, write down the letters used to refer to each axes and the origin and the numbers that are given on the axes.

3. POINTS AND PAIRS OF NUMBERS
This system of reference can be used to determine the position of any point on a set of axes by an ordered pair of numbers, which are usually written in brackets and separated by a comma. At the beginning of this activity the red point is located at the point (2,3).
Use the red and blue arrows (x and y) to move the point or write the number in the white box and press the Enter key.

5.- Move the red point to the following positions:

(2,5) (-3,2) (-5,-2) (-3,0)
(10,3) (7,-10) (0,5) (20,16)
(40,35) (-30,40) (1,-1) (-15,0)
 
Change the scale or move the axes if necessary.
6.-Make up six pairs of whole numbers and plot the corresponding points on a set of axes in your notebook; try and locate them in different parts of the plane. Then, check that you have plotted them correctly by using this window.
4. ABSCISSA AND ORDINATE COORDINATES OF A POINT.  ( x , y )
The numbers in each ordered pair of numbers are called the coordinates of the corresponding point. The first number is called the x-coordinate (or abscissa) and the second the y-coordinate (or ordinate).

7.- Move the red point to the different quadrants on the plane and look carefully at its coordinates (x,y).

You can also move the point by selecting it with the mouse and dragging it or by using the arrow buttons.

8.-In your notebook write the sign given for the x and y-coordinates in each of the quadrants.

9.-In your notebook indicate in which quadrants both of the coordinate numbers have the same sign and in which quadrants the signs are different.
       
           
  Juan Madrigal Muga
 
Spanish Ministry of Education. Year 2001
 
 

Licencia de Creative Commons
Except where otherwise noted, this work is licensed under a Creative Common License