The foot and image of a point in a plane in 3D

Direct answer

Move a point and a plane in 3D and see the distance, the foot of the perpendicular and the image of the point in the plane.

Drop a perpendicular from P to the plane: where it lands is the foot. Go the same distance again beyond the plane to reach the image (mirror point).

Simulation

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Foot and Image of a Point in a Plane (3D)

3D geometry

a 1

b 1

c 1

d 3

Point P: x 3

Point P: y 2

Point P: z 3

Drag to rotate, two fingers or right-drag to pan, scroll or pinch to zoom. The toolbar has views, cutaway, measure and “show the maths”.

What's happening? Drop a perpendicular from P to the plane: where it lands is the foot. Go the same distance again beyond the plane to reach the image (mirror point).

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Where it is in NCERT: Class 12 Mathematics Part II, “Three Dimensional Geometry” (Direction Cosines and Direction Ratios of a Line, Equation of a Line in Space, Angle between Two Lines, Shortest Distance between Two Lines) · ncert.nic.in
Topic notes and formulas: Three Dimensional Geometry
Printable formula sheet
Chapter-wise JEE Main PYQs (17)