Coordinate systems are indispensable aids, if one wants to solve geometrical problems with computational means or vice versa wants to interpret geometrically the results - homework help at Do My Homework Club , which resulted from the treatment of certain problems with computational methods. In this sense, coordinate systems are, as it were, links between geometry and arithmetic, which, moreover, often make it possible in the first place to make certain practical, "extra-mathematical" facts accessible to mathematical processing, to "model" them mathematically.
A coordinate system of the plane consists of two number lines intersecting each other in the zero point - the coordinate origin O -, whereby one line is called abscissa axis (as a rule also x-axis), the other one ordinate axis (as a rule also y-axis). On each axis a coordinate unit point different from O is defined.
If the two axes are perpendicular to each other, they form a rectangular coordinate system - do do my math hw for me . A Cartesian coordinate system exists if, in addition, the unit distances on both axes are the same in a rectangular coordinate system.
It is determined that the directed x-axis changes into the directed y-axis on the shortest way when rotating counterclockwise (thus in the mathematically positive direction of rotation - algebra homework help ). One says then: The x- and the y-axis form a right system.
With the help of a coordinate system, each point P of the plane can be uniquely assigned an ordered pair of numbers - the coordinates of this point. The first coordinate (x-coordinate, x-value or absizissi of P) indicates how far away the point P is from the right or left of the y-axis. The second coordinate (y-coordinate, y-value or ordinate of P) tells how far P lies above or below the x-axis. Conversely, for each pair of numbers (x; y) there is a point P in the plane which is uniquely determined by this and which then has the coordinates x and y (interactive calculation example).
By each of the coordinate systems described above the plane is divided into four quadrants. It is valid for the points
of the I. quadrant: x > 0 and y > 0, of the II. quadrant: x < 0 and y > 0, of the III. quadrant: x < 0 and y < 0, of the IV. quadrant: x > 0 and y < 0.
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