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.

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)"