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Plane definition in Math

What is a Plane in Math?

In mathematics, a plane is a two-dimensional flat surface that extends infinitely in all directions. It is often represented as a flat sheet of paper or a coordinate grid with an x-axis and y-axis.

A plane can be defined by three non-collinear points, or by an equation in the form of Ax + By + Cz + D = 0, where A, B, and C are constants and x, y, and z are variables representing the coordinates of any point on the plane.

In geometry, a plane is used to describe various shapes such as triangles, rectangles, and circles. The study of planes and their properties is an important part of geometry and other areas of mathematics, such as calculus and linear algebra.

A plane has

  • zero curvature,
  • zero thickness,
  • infinity length
  • and infinity width.

With the help of length and width, we make a plane.


Properties of Planes

Here are given some properties of planes in mathematics:

  1. Infinitely Extending Surface
  2. Defined by Three Non-Collinear Points
  3. Intersecting Planes
  4. Distance between a Point and a Plane
  5. Parallel Planes
  6. The angle between Two Planes
  7. Transversal

How do you make a Plane?

A plane can be formed by a three-dimensional space.

(a) Point:- A point has zero dimensions. A point denotes an exact location on a plane.


(b) line:- A line is a combination of infinite points. A line segment has two defined endpoints. It is a one-dimensional straight figure.


For Example:-

Example 1: Sophie, a teacher, is asking her students. Are points A, B, C, and D  coplanar?

plane example


According to the definition of coplanarity, points lying in the same plane are coplanar. Points A, B, C, and D lie in the same plane.∴ Yes, points A B, C, and D are coplanar.