The system of coordinates is a set of two and more crossed axes of coordinates, with single pieces on each of them. The beginning of coordinates is formed in a point of intersection of the set axes. Coordinates of any point belonging to this system of coordinates define its location. To each point there corresponds only one set of coordinates (for the nondegenerate system of coordinates).
Instruction
1. The system of coordinates is called rectangular (orthogonal) if its axes of coordinates are mutually perpendicular. If at the same time they are also divided into pieces (units of measure), equal on length, then such system of coordinates is called Cartesian (orthonormalized). The course of high school includes consideration of a two-dimensional and three-dimensional Cartesian system of coordinates. If t. About – a reference mark, OX axis – an abscissa, OY – ordinate, OZ – z-coordinate.
2. Let's review a simple example of calculation of coordinates for points of intersection of two set circles. Let O1, O2 be the centers of circles with the set coordinates (x1; y1), (x2; y2) and known radiuses of R1, R2 respectively.
3. It is necessary to find coordinates of points of intersection of these circles of A (x3; y3), B (x4; y4), and t.D – a point of intersection of pieces of O1O2 and AB.
4. Decision: for convenience we will accept that the center of the first circle O1 coincides with the beginning of coordinates. Let's consider further simple crossing of the circle and straight line passing through AB piece.
5. According to R2 circle equation = (x1-x0) 2 + (y1-y0) 2, where O (x0; y0) – the center of a circle, A (x1; y1) – a point on a circle, we will work out the system of the equations at x1, y1 equal to zero: R12 = O1O2+OA2 = x3 + y32, R22 = O1O2+OA2 = (x3 - x2) 2 + (y 3 - y 2)2
6. Having solved a system, we will find A point coordinates, similarly there are B point coordinates.