Coordinates

Coordinates

plane x,y

We shall take two mutually perpendicular axes X and Y on a plane, with their point of intersection O as origin on each (Fig. 3). The positive directions on the axes are shown by arrows. We have a real number, denoted by the letter x, corresponding to a point of the axis X. Similarly, a real number denoted by y corresponds to a point of the axis Y. If specific values are assigned to x and y, points A and B are defined on axes X and Y; knowing A and B, we can construct the point M as the intersection of lines parallel to the axes and passing through A and B.

position of point

To each pair of values x, y, there corresponds a single fully defined position of the point M on the plane of the figure. Conversely, to each point M of the plane there corresponds a fully defined pair of values of x, y
corresponding to the points at which lines through the point M parallel to the axes intersect the axes X and Y. With the directions of the axes shown in Fig. 3, x is to be reckoned positive or negative, depending on whether A lies to the right or left of point O;
 similarly, y is positive or negative, depending on whether B lies above or below, point O.
 The magnitudes x, y defining the position of point M in the plane, and defined in turn by point M, are called the coordinates of M. The axes X, Y are called the coordinate axes, the plane of the figure is the plane 
of coordinates XOY, and the point O is the origin of coordinates. Magnitude x is called the abscissa, and y the ordinate, of the point M. We shall specify the point M by its coordinates by writing: M(x, y). This method of representation is called the method of rectangular coordinates. The signs of the coordinates of the point M when situated in different quadrants of the axes (I-IV) (Fig. 3) can be shown in a table:

It is obvious that the coordinates x, y of M are equal to the distances of M from the coordinate axes, associated with the corresponding signs.

the source:

A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.

By: Fady tarek