If the descriptive geometry is a theoretical base of drawing, then creation of a point in space on coordinates – fundamentals of geometry. The provision of any point in space can be set three coordinates, and if you have three planes of projections, you cannot find it.
It is required to you
- - point with coordinates (a, b, c);
- - system of coordinates.
Instruction
1. Construct three coordinate planes to have a reference mark in a point of the Lake. On the drawing of the plane of projections are designated in the form of three axes – oh, ou and oz, and an axis of oz is directed up, an axis ou – to the right. To construct the last axis oh, divide a corner between axes ou and oz in half (if you draw on the squared paper sheet, just carry out this axis on diagonalsof cages).
2. Pay attention if coordinates of a point And are written down in the form of three numbers in brackets (and, b, c), that first and – distance from the plane x, the second b – from at, the third with – from z. At first take the first coordinate and and note it on an axis oh, to the left and down if number and positive, to the right and up if it is negative. Call the received letter Century.
3. Further take number b and postpone it for axes ou – to the right if it positive, and to the left if it is negative. Call noted point letter C.
4. Then postpone the last number with up oz axis if it positive, and down the same axis if negative. Note the received point letter D.
5. From the received points carry out traces of projections of a required point on the planes. That is in a point In draw two straight lines which will be parallel to axes ou and oz, in a point With draw the straight lines parallel to axes oh and oz, in a point of D – the straight lines parallel oh and ou.
6. Two straight lines drawn in one plane will be crossed. Restore in this place a perpendicular (from all three planes) to find a required point. As a result you receive the drawing of a parallelepiped, note a point letter A. Check, distances to the planes of this point are equal and, b, page.
7. If one of coordinates of a point is equal to zero, so the point lies in one of the planes of projections. In that case just note the known coordinates on the plane and find a point of intersection of their projections. Be attentive at creation of points with coordinates (and, 0, c) and (and, b, 0), do not forget that the projection to an axis oh is carried out at an angle in 45 ⁰.