Determine the distance from a point to a plane
In this paper we consider two similar problems for determining the distance from a point to a plane.
Take the 1 and 6 options for which you need to determine:
- The distance from the point D to the plane defined by the triangle ΔABC.
- Visibility of the perpendicular passing through the point D and the plane of the triangle ΔABC.
- The natural value of the perpendicular passing through the point D to the plane of the triangle ΔABC.
Given:
The coordinates of the vertices of triangle ΔABC and point D.
Coordinate value table.
Option | Coordinate values, mm | ||||||||||||||
X_{A} | Y_{A} | Z_{A} | X_{B} | Y_{B} | Z_{B} | X_{C} | Y_{C} | Z_{C} | X_{D} | Y_{D} | Z_{D} | X_{E} | Y_{E} | Z_{E} | |
1 | 170 | 120 | 80 | 140 | 45 | 135 | 70 | 60 | 50 | 185 | 45 | 55 | 60 | 70 | 75 |
6 | 10 | 60 | 130 | 150 | 10 | 90 | 70 | 100 | 50 | 150 | 100 | 130 | 20 | 40 | 90 |
The solution of problems on descriptive geometry I produce in the automated design system AutoCAD and AutoCAD 3D. This training will allow you to develop spatial thinking and consolidate the possession of AutoCAD.
Algorithm for solving the problem of descriptive geometry "Determining the distance from a point to a plane":
- Construction of the plane ABC and point D in absolute rectangular coordinates;
- Construction of the horizontal and front surfaces of the plane;
- Construction of a perpendicular to the plane;
- Finding the intersection point of the perpendicular (straight) with the plane;
- Determination of the visibility of the perpendicular (straight) and the plane by the method of competing points;
- Finding the natural value of a perpendicular (straight) by the method of a right-angled triangle (distance from a point to a plane).
Solution of problem 1 of the variant for determining the distance from a point to a plane
Draw the coordinate axes XYZ. We put the coordinates of the points A, B, C, which define the plane α and the point D, through which the perpendicular to the plane will pass.
Solution of problem 6 of the variant for determining the distance from a point to a plane
Draw the coordinate axes XYZ. We put the coordinates of the points A, B, C, which define the plane α and the point D, through which the perpendicular to the plane will pass.
Video "Distance from point to plane - perpendicular to plane (Russian)"
Video "Distance from a point to a plane (continued) Russian"
Video "Determine the distance from the point to plane 6 variant (Russian)"
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