37. Rectangular coordinates of points

The three main projection planes (P ₁ _ | _P ₂ _ | _ P ₃ ) can also be considered as coordinate planes. Then the axes of the projections become the coordinate axes: the x- axis x, P ₁ / P ₃ —an axis of coordinates y, P ₂ / P ₃   —Other application z.

The origin (point O) is located at the point of intersection of the axes of the coordinates (Fig. 68, a).

To assign point A to the natural coordinate system Oxyz, it is necessary to construct an orthogonal projection of point A on the xOy plane . Then the projection A _{1 is} orthogonal to the projection on the x axis to the point A _x . Then we get the spatial coordinate polyline AA ₁ A _X O, the segments of which are parallel to the axes of coordinates and, accordingly, are called: OA _X - the abscissa segment; And _Х А ₁ - ordinate segment; And ₁ And - a segment of applicati.

Measuring the coordinate segments of a unit of length l , we obtain three abstract numbers - three coordinates of point A:

x = OA _X abscissa; y = A _x A ₁ - ordinate; z = AA ₁   - applicate.

If a point is given by its own coordinates A (x, y, z), then it is possible to construct its complex drawing by specifying the corresponding unit of length l (for example, l = 1 mm). The abscissa of the point determines the position

Fig. 68

vertical communication line (Fig. 68, b). The horizontal projection of a point is determined by the magnitude of the ordinate, and the frontal projection is determined by the magnitude of the applicants.