How to build a point with three coordinates

If descriptive geometry is the theoretical Foundation drawing, build a point in space on coordinate – based geometry. The position of any point in space, you can specify three coordinates, and, if you have three planes of projections, you will not be difficult to find her.

You will need

• - the point with coordinates (a,b,c);
• - coordinate system.

Instruction

1. Draw the three coordinate plane to have the origin at the point O. In the drawing, the plane of projection are designated by three axes Oh, Oh and oz, the axis oz directed upwards, the axis of the shelter to the right. To build the latest ox-axis, divide the angle between the axes OU and oz in half (if you draw on paper, just slide the axis on the diagonal cells).
2. Please note, if the coordinates of point A are written as three numbers in brackets (a, b, C), then the first number a is the distance from the plane x, the second by b – have, a third c – z. First, take the first coordinate and mark it on the ox axis, to the left and down if the number is positive, right and up, if it is negative. Received the letter V. name
3. Next, take b and place it on the axis Oy – the right positive and left if negative. Name the marked point with the letter S.
4. Then put the last number with the up axis oz, if it is positive, and down on the same axis, if negative. Mark received a dot letter D.
5. From the points guide the traces of the projections of the required point on the planes. That is, at point b, draw two straight lines which are parallel to the axes OU and oz, at the point C draw straight, parallel to the axes ox and oz, at the point D is straight, parallel to Oh, and Oh.
6. Two straight, held in the same plane, intersect. Restore the normal (all three planes) to find the desired point. As a result, you will receive a drawing of the box, mark the point with the letter A. Check the distance to the planes this point is equal to a, b, C.
7. If one of the coordinates equal to zero, then the point lies in one of planes of projections. In this case, just check the known coordinates of the plane and find the point of intersection of their projections. Be careful when you build the points with coordinates (a, 0) and (a, b, 0), do not forget that the projection on the axis ox is at an angle of 45⁰.