Can anyone teach me cartsian coordinates fully?please?

1 Answer
Apr 30, 2016

Below is a short description of Cartesian coordinate system.


Cartesian coordinates are by far the most common type of coordinates used in mathematics.

To numerically identify a point on a line we fix one particular point called the beginning of the coordinates or origin, one particular direction on this line from the origin which we call the positive direction and some unit of measurement represented as a segment we set as having the length of #1#.

Now we are ready to put into correspondence for any point on this line a number that characterizes the distance from this point to the origin measured in the units we have set and with a sign depending on whether the point lies towards the positive direction from the origin or the opposite negative one. For a point positioned exactly at the origin this number is of course zero. This number is called a point's coordinate. Since we need just one number to identify a point on a line in our system, the line is called a one-dimensional space.

To identify a point on a plane, we have to fix a pair of mutually perpendicular lines usually called X-axis and Y-axis that divide a plane into four quadrants. On each of these lines we can set a one-dimensional Cartesian coordinates with the origin at a point of intersection of these lines. Each point on a plain can now be projected to both axes by dropping from it perpendiculars to them.

Now we have two projection points - one on the X-axis and another on the Y-axis. These projection points have one-dimensional coordinates on the corresponding axes. One is called X-coordinate or abscissa, another - Y-coordinate or ordinate. A pair of these coordinates constitute coordinates of the original point on a plane.

The quadrant with points having positive X- and Y-coordinates is called the first quadrant. Then other quadrants are numbered counterclockwise - second (negative X, positive Y), third (negative X, negative Y) and forth (positive X, negative Y). Since we need two numbers to identify a point on a plane, the plane is called a two-dimensional space.

To identify a point in our space where we live, the Cartesian coordinates are defined as a triplet of one-dimensional coordinates of projections of our point to three mutually perpendicular lines usually called X-axis, Y-axis and Z-axis sharing the origin. These three coordinates are called abscissa (on the X-axis), ordinate (on the Y-axis) and applicate (on the Z-axis). Since we need three numbers to identify a point in our space, our space is called three-dimensional.

Multi-dimensional spaces with more than three dimensions are also studied in mathematics. They have a limited visual representation but are very useful in solving many practical problems.

For more information you can go to UNIZOR Web site and examine the topic Math Concepts - Coordinates.