The rectangular or orthogonal system of coordinates call a set of mutually perpendicular coordinate axes. In two-dimensional - flat - space of such axes two, in three-dimensional - volume - three. It is theoretically possible to imagine any number of measurements. Except axes an important element of a system is the single piece of each of them - it sets the scale of units in which coordinates of any point are measured in space.
It is required to you
- Drawing, pencil, ruler.
Instruction
1. If the end is put to the drawing on which there is also a coordinate grid or at least coordinate axes with the single pieces noted on them, for determination of its coordinates carry out couple of auxiliary pieces. One of them has to be parallel to abscissa axis, begin in a point which coordinates are defined, and to come to an end on ordinate axis. Abscissa axis usually call horizontally located axis with the values increasing from left to right - designate it by letter X. Ordinate axis is perpendicular to it and is directed from bottom edge of a leaf to top - it is designated by letter Y.
2. Measure length of the carried-out horizontal auxiliary piece. Not always divisions of a system of coordinates coincide from them of centimeters therefore it is necessary to measure lengths in those units which are set by single pieces on coordinate axes. If the point is located to the left of a vertical axis, the measured size should be considered negative. Length of this piece parallel to axis X taking into account the sign determines the first coordinate of a point - an abscissa.
3. Carry out the second auxiliary piece. It has to be parallel to ordinate axis, begin in the measured point and come to an end on abscissa axis. Determine its length by the same rules, as in the previous step. The received size will give the second coordinate of a point - ordinate. If the point is located below a horizontal axis, before this size it is necessary to put minus. Having received couple of values, you determine rectangular coordinates of a point in a two-dimensional Cartesian system. For example, if for some point A the measured sizes along axes X and Y are equal 5.7 and 8.1 respectively, its rectangular coordinates can be written down so: A(5,7;8,1).
4. In the three-dimensional rectangular system of coordinates the third axis - an axis of z-coordinates is added to abscissae and ordinates. It is usually designated by letter Z, and in a set of the numbers setting position of a point in space costs on the third position - for example, A(5,7;8,1;1,1).