The geometrical figure can be represented rotating, that is holding a certain position in relation to the motionless system of the planes of a projection. As an axis of rotation any straight line can be used. Knowing basic data of the rotating figure, it is possible to determine its full size and also to find distance from the set point to a triangle.
It is required to you
- - textbook "Geometry";
- - ruler;
- - simple pencil;
- - notebook.
Instruction
1. Solve this problem by replacement of the planes of a projection. The direct planes passing perpendicularly to lines of level of this plane in geometry received name lines of the greatest inclination of the plane to the plane of projections corresponding to it. Carry out in the drawing a horizontal of h and frontal by f. In view of the fact that the line of the greatest inclination of the plane is the perpendicular plane of a projection P1 (this perpendicularity is kept on a horizontal projection), its horizontal projection will pass through C1 point, that is perpendicular to h1 projection. As the line of the greatest inclination is perpendicular to P2 plane projection, the frontal projection of a triangle has to be perpendicular to f2 projection.
2. To transform the projecting plane to the level plane, construct one more plane of projections: it has to be located parallel to a triangle projection with tops of A4, B4 and C4. Then draw binding lines and postpone coordinates of points which are taken from P1 plane. The projection of a triangle of A5B5C5 received in the drawing will correspond to the full size of a triangle of AVS.
3. Having found the full size of a triangle of ABC, with ease you will be able to define distance from a certain point of D to a triangle. For this purpose lower a perpendicular from a point of D on the plane of that projection which is projecting. After that find length of the lowered perpendicular.