Distance from point to a plane.

Title: Distance Between a Point and a Plane

Description:
In this lesson, we explain how to calculate the shortest distance from a point in 3D space to a given plane. You’ll learn:

The general equation of a plane: Ax + By + Cz + D = 0

The coordinates of a point: P(x₁, y₁, z₁)

The formula for distance:


d = \frac{|Ax₁ + By₁ + Cz₁ + D|}{\sqrt{A^2 + B^2 + C^2}}

Step-by-step derivation of the formula

Geometric interpretation of why this formula gives the perpendicular (shortest) distance

Worked-out examples to build intuition


This topic is essential in 3D Geometry for competitive exams, higher mathematics, and applications in physics and engineering.