Coordinate system. Coordinate quarters

In everyday life, you can often hear the phrase: "Leave me your coordinates." In response, the person usually leaves his address or phone number, that is, the data by which it can be found.

Coordinates can be designated by the most different sets of numbers or letters.

For example, the car number is the coordinates, because by the car number you can determine from which city it is and who its owner is.

Examples of coordinates are: the number of the car and the place in the train, the latitude and longitude on the geographical map, the recording of the position of the piece on the chessboard, the position of the point on the number axis, etc.

Whenever, according to certain rules, we unambiguously denote an object by a set of letters, numbers, or other symbols, we specify the coordinates of the object.

Cartesian coordinate system

The French mathematician Rene Descartes (1596 - 1650) suggested specifying the position of a point on a plane using two coordinates.

To find the coordinates, we need reference points from which the reading is taken.

• On the plane, such reference points will be two numerical axes. In the drawing, the first axis is usually drawn horizontally, it is called the axis of the APSCIS and is designated by the letter X, the axis Ox is written. The positive direction on the x-axis is chosen from left to right and indicated by an arrow.
• The second axis is carried out vertically, it is called the ORDINAT axis and is denoted by the letter Y, the axis Oy is recorded. The positive direction on the y-axis is chosen from the bottom up and shown by the arrow.

The axes are mutually perpendicular (i.e. the angle between them is 90 °) and intersect at the point that is designated O. The point O is the starting point for each of the axes.

Coordinate axes are straight lines forming a coordinate system.

The abscissa axis (Ox) is the horizontal axis.

The ordinate axis (Oy) is the vertical axis.

Coordinate plane - the plane in which the coordinate system is built. Denoted by the plane as x0y.

We draw your attention to the choice of the length of single segments along the axes.

Figures denoting numerical values ​​on the axes can be placed both to the right and to the left of the Oy axis. The numbers on the Ox axis, as a rule, are written below the axis.

Usually a single segment on the 0y axis is equal to a single segment on the 0x axis. But there are times when they are not equal to each other.

The coordinate axes divide the plane into 4 corners, which are called coordinate quarters . The quarter formed by positive semiaxes (upper right corner) is considered the first (I).

Count the quarters (or coordinate angles) counterclockwise.