At the solution of topographical, physical and mathematical tasks often it is required to determine rectangular coordinates of an object or point. The Cartesian rectangular coordinates of the point located on the plane are called distances between this point and two mutually perpendicular straight lines. If the point is in space, then distances are measured to three mutually perpendicular planes.
It is required to you
- - ruler;
- - compasses;
- - drawing triangle with a right angle.
Instruction
1. For determination of rectangular coordinates of a point on the plane, lower perpendiculars from this point on an axis of coordinates. As a rule axes of coordinates have and designate as follows: • an axis abscissaeof located it is horizontal, it is directed to the right, it is designated as OH; • ordinate axis it is located vertically, directed up, it is designated as OY.Rasstoyaniya from points of intersection of perpendiculars prior to the beginning of coordinates are point coordinates on the plane. The perpendicular point of intersection with an axis OH is called an abscissa and is designated through x, and the perpendicular point of intersection with an axis of OY is called ordinate and is designated usually through y.
2. To determine rectangular coordinates of a point in space, carry out pe perpendiculars on three axes of coordinates. Usually these axes have the following arrangement and designation: • abscissa axis is located perpendicular to the drawing plane, directed to the observer and is designated as OH; • ordinate axis is located vertically, directed up and is designated as OY; • the axis of z-coordinates is located vertically, directed up and is designated as OZ.Dlya determination of the corresponding coordinate it is necessary, as well as in the first point, to carry out to each of coordinate axes a perpendicular. Then to measure distance from a perpendicular point of intersection with the corresponding axis prior to the beginning of coordinates.
3. To determine rectangular coordinates on the topographic map: • define a square in which there is a point; • on South side of this square find and write down full value of an abscissa (x) in kilometers; • measure by compasses, a ruler or a koordinatomer distance on a perpendicular from a point on the map to this coordinate line and add it to an abscissa (the distance is measured in meters). Calculation of ordinate of a point on the topographic map is made similarly – only instead of South side of a square the West side is used.