FUNCTIONS AND GRAPHS I
Cartesian coordinates
Organization of the plane.
René Descartes, a French philosopher and mathematician (1596-1650) bases his philosphical thought on the need of taking a point from which to construct all knowledge: I think then I exist. In mathematics, he is the creator of analytical geometry, constructed also by taking a starting point and two perpendicular straight lines which intersect at this point. This construction is called a Cartesian coordinate system.
1.- Move the mouse over the rectangle above, click the main button and see what happens. The emphasized white sraight lines are called Axes and the point in which they intersect is called the Origin.
The Cartesian Plane
The horizontal axis is called the X axis and the vertical one is called the Y axis.
2.- Change the scale and move the axes to see that with the reference system (O;X,Y) all the points on the plane can be "named". (Use the coloured arrows or write the values that you want in the text fields of the scale, of Ox and of Oy. The Init button returns to the initial conditions.)
Points and pairs of numbers.
With this reference system each point on the plane can be "named" with two numbers, which are usually written in parentheses and separated by a comma.
On starting this activity the red point is in (2,3).
3.- Displace the red point to the following positions using the arrows or writing the numbers. (Use the changing scale or move the axes when you need to.)
(2,5), (-3,2), (-5,-2), (-3,0), (10,3), (7,-10), (0,5), (20,16), (40,35), (-30,40), (1,-1)
Invent pairs of whole numbers and put the point in the corresponding positions.
Coordinates of a point: abscissa and ordinate.
The numbers of each pair are called coordinates of the respective point, the first number is called abscissa and the second ordinate.
