What is Point in Geometry –  Definition, Types & Examples

Let’s learn about Point!

What is Point in Geometry –  Definition, Types & Examples

Definition of point in geometry is well explained, along with simple explanation, different types of points, examples, etc. Let’s explore the point!

What is a Point in Geometry?

Points Geometry Basics

Point is a tiny word that doesn’t have any size except the position.

  • Points are denoted by capital letters ‘’P’’, or ‘’Q’’ or ‘’R’’ etc.
  • The point is represented as a dot.
  • It doesn’t have any length, width or height, or thickness.
  • If two straight lines are intersected, the position at which intersection happens is known as point.

Definition of Point in Geometry

Point is defined as a position that doesn’t have any size or thickness.

what is point in geometry definition examples
What is point in geometry definition examples

Dimension of a point

There were so many confusions on the dimension of a point. Finally, it is concluded as 0- dimensional position.

Types of Points

Points are classified into few types,

  • Colinear point
  • Non-colinear point
  • Concurrent point
  • Coplanar point

Colinear Points

Collinear Points Definition

As the name suggests, colinear means linear. The points which are in a linear section or on a straight line, are known as collinear points.

Col means together in Latin word. So, collinear means col + linear means points together in a linear way.

Let’s consider, point P, Q, R, S on the straight line, as below.

points in geometry collinear points
Points in geometry collinear points

Collinear Point Examples

Collinear points can be easily understood with a very simple example. We all have learned that light travels in a straight line and a candle experiment has been done.

In that experiment, we have seen that all the points (P, Q, R, S) are positioned in a straight line.  Here come the collinear points, as all points are in the same straight line.

On a single bench, you along with your friends are sitting

Non-collinear Points

Non-collinear Point Definition

As the name suggests, non-collinear means non-linear. The points which are not on in a linear section or not on a straight line, are known as non-collinear points.

points in geometry non collinear points
Points in geometry non collinear points

Let’s consider, points P’, Q’,  as non-colinear points.

Non-collinear Point Examples

Non-collinear points can also be explained with a very simple example. If you take few points and try to draw a single straight line and but you are not able to make it, then these points are non-collinear points.

Concurrent Points

Concurrent Points Definition

When two or more lines are intersected at a point, is called a concurrent point.

Let’s consider, point P, Q, R, S, and the line between P-R and Q-S intersected at point A. This point A is called a concurrent point.

Concurrent Points Examples

Let’s see an easy example of concurrent points. We all know kites and also spent time flying the kites.

points in geometry concurrent points
Points in geometry concurrent points

If you see the structure of the kite, you will see two sticks are crossed and intersected at a point. This point is known as the concurrent point.

Coplanar Points

Coplanar Point Definition

Coplanar, as the name implies, means the points lie on a plane.

  • To check coplanar points, there should be a minimum of three points.
  • All three points are coplanar based on the three-dimensional figures.

Here, point A, B, C, D all are on a single plane. So, these points are coplanar points.

points in geometry coplanar points
Points in geometry coplanar points

Coplanar Point Examples

Take four points on a table, it means all the points are on the table surface. So, these points are coplanar points.

Difference between Collinear vs. Coplanar

Collinear Points Coplanar points
All points on a line All points on a single plane
Points on a straight line are  examples Points a single plane are examples.

Interesting Philosophy about a Point

There are so many interesting philosophies existed about points, these are,

  • The point means a dot and you can make it 1mm diameter but still, it will not have any size or dimension.
  • Any numbers it may be 5000 or even 5,00,000, a point can make it 0.5 with its position.

Exercise on Points in Geometry

Refer to the below diagram and try to solve the small exercise.

points in geometry exercise
Points in geometry exercise
  • Identify the points.
  • Identify the points which are collinear.
  • Identify the points which are non-collinear.
  • Identify the points which are coplanar.

Solution

Points A, B, C, D, E, F, G, and H are simple dots that don’t have any dimension. These are points.

The following points lie on the same straight line and we already learned that if points lie on the same line is called collinear points,

  • ACE
  • AGF
  • CGH

Points B, and D are not on the same line and these are colinear points. The following points are on the same plane and we already learned that if points lie on the same plane is called coplanar points,

  • ACFH
  • ACFG
  • ACG
  • CFG
  • AGFH
  • AGH
  • FGH

Conclusion

Hence, we have got a basic idea about what is point in geometry. Any comments, please let us know.

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