How to find distance from point to plane

To find distance from point to plane:• swipe through this point a straight line perpendicular to that plane;• find the base of the perpendicular is the intersection of a line with a plane;• measure the distance between the given point and the base of the perpendicular.

For finding the distance from point to plane methods of descriptive geometry:• select the plane of an arbitrary point;• swipe through it two straight (lying in this plane);• restore the perpendicular to the planepassing through this point (build the line, is perpendicular simultaneously to both intersecting straight);• swipe through a given point parallel to the straight line constructed perpendicular;• find the distance between the point of intersection of this line with the plane and a given point.

If the provision point is set to its three-dimensional coordinates, and the position of the plane is a linear equation to find distance from plane to point, use the methods of analytic geometry:• identify coordinates of a point using x, y, z, respectively (x is the abscissa, y ordinate, z – applicate);• designate by A, b, C, D the parameters of the equation of the plane (A is the parameter with the x coordinate, and V – At y-point, – when you applicate, D – free term);• calculate distance from point to plane formula:s = | (Ax+By+Cz+D)/√(A2+B2+C2) |,where s is kastanie between a point and a plane|| - the designation of absolute value (or modulus) of a number.

Example.Find the distance between point a with coordinates (2, 3, -1) and the plane given by the equation: 7x-6U-6z+20=0.Solution.Because of the problem it follows that:x=2,y=3,z=-1,A=7,B=-6,C=-6,D=20.Substitute these values into the formula above.Work:s = | (7*2+(-6)*3+(-6)*(-1)+20)/√(72+(-6)2+(-6)2) | = | (14-18+6+20)/11 | = 2.Answer:the Distance from the point to the plane is 2 (standard units).