In modern mathematics a point are called elements of the very different nature of which various spaces consist. For example, in n-dimensional Euclidean space a point is called the ordered set from n of numbers.
It is required to you
- Knowledge of mathematics.
Instruction
1. A straight line - one of the basic concepts in mathematics. Analytically the straight line on the plane is set by the equation of the first order of a type of Ax+By=C. It is easy to define point belonging to the set straight line, having substituted point coordinates in the straight line equation. If the equation addresses in right equality, the point means belongs to a straight line. For example, we will consider a point with coordinates of A(4, 5) and the straight line set by the equation of the 4th +3u =1. Let's substitute in the equation of direct coordinate of a point And yes we will receive the following: 4*4+3*5 = 1 or 31 = 1. Received equality which is not true, so, this point does not belong to a straight line.
2. For search of a point on a straight line it is enough to take one of coordinates and to substitute in the equation, and then to express from received the equation the second. Thus there will be a point from the set one of coordinates. As the straight line passes through all plane, and points which belong to it infinitely much, so, for any one coordinate there will always be another, such that the received point will belong to the set straight line. Let's take for an example a straight line with the equation 3x-2y=2. Also we will take coordinate equal x=0. Then we will substitute value x in the equation of a straight line and we will receive the following: to a 3*0-2 =2 or at =-1. Thus we found the point lying on a straight line and its coordinates are equal (0,-1). The same way it is possible to find the point belonging to a straight line when y coordinate is known.
3. In three-dimensional space at a point 3 coordinates, and the straight line is set by a system from two linear equations of a type of Ax+By+Cz=D. The same way, as well as in a two-dimensional case if you know at least one coordinate of a point, having solved a system, you will find two others and this point will belong to an initial straight line.