Learn to build symmetric points at geometry lessons at high school. This ability can be useful further at drawing lessons and also on classes in higher educational institutions.
Instruction
1. Read a statement of the problem and define concerning what the point has to be symmetric. For example, creation of a point symmetric concerning other point, an axis of symmetry, the beginning of coordinates, axes Okh or Ou, etc. can be required.
2. If you need to construct A1 point symmetric And concerning the beginning of coordinates, at first determine coordinates of a point And. A1 will have the same coordinates, but with the opposite sign. For example, A1 (3;-5) it will be symmetric And (-3; 5). Find and construct on graphics A1 point with the received coordinates.
3. To construct A1 point symmetric And concerning an axis Oh, it is necessary to find a point with the same abscissa, but at the same time with the ordinate opposite according to the sign. It means that to a point And (x; s) A1 will be symmetric (x; - у). For example if And has coordinates 6 on an axis Oh and 2 on Ou's axis, then you will need to find and construct A1 point (6;-2).
4. If it is required to construct A1 symmetric And concerning Ou's axis, find A1 which ordinate will be equal And, and the abscissa is opposite to an abscissa And according to the sign. It means that A1 (-x; s) it will be symmetric And (x; у). For example, if it is given And (4; 8), it is necessary to find and construct A1 (-4; 8).
5. If it is necessary to construct A1 point symmetric And concerning a point In, then it is necessary to draw at first a beam from And, passing through V. Izmerte distance from And to In and construct A1 point at the same distance from In, but in the opposite direction of a beam. As a result at you the piece of AA1 which center is the point of Century will turn out.
6. To construct A1 point symmetric And rather direct, construct a beam with the initial point And, crossed about direct and perpendicular to it. Measure distance from And to a point of intersection of a straight line and a beam, and then construct A1 point at the same distance from a straight line, but in the opposite direction. At you the piece of AA1 which is halved by a straight line exactly has to turn out.