# What is Point in Geometry ? Point in Geometry Definition, Types, and Examples

## Definition

In geometry, a point is a fundamental unit without any quantitative attributes such as size: width, length, height and depth etc. The point only represents a position or location of a variable in plane marked by a dot (.) and is preferably denoted with a capital letter (P, Q, A etc.).

## Line or Line Segment

Only when point is extended infinitely or indefinitely in two directions, then point is termed as line or more precisely line segment. A line has infinite length without any width and height i.e., a line is one-dimensional. In 2-dimensional Euclidean geometry, a point is represented by a pair of numbers which is always ordered e.g., (x,y). Here x represents the horizontal, whereas y indicates the vertical component of a plane. In 3-dimensional space, a point is represented by an order of triplet e.g., (x,y,z) in which the third component is added to the space in which a point is located.

#### Real-life Examples

For better understanding, the real-life examples of a point can be a star in the sky, the pointed end of a needle, or tip of a ball point etc.

## Dimensions of a Point

As discussed above, a point is free of any dimension as it doesn’t own any measurable property. A point itself is zero dimensional and can possess quantitative property only when it is extended in at least one direction; thereby producing a line. One value is required in order to identify the point on line which will provide one dimension or making a line one dimensional.

Similarly, if point is extended to two directions, two values are required to find the point on plane; which creates two dimensions (2D) as seen in circle, square etc. Likewise, if a line is stretched to entirely different direction other than horizontal or vertical components, a new third value is identifiable to find the location of point, giving it three dimensions (3D) as found in sphere, cube etc.

#### Real-life Examples

For better understanding, the real-life examples of 2D figures are chessboard, a piece of paper or a pizza. The 3D figures could be basketball, cylinder or an egg etc.

### Type of Points

A point can be classified into a few types which are as explained below:

- Collinear Points
- Non-collinear Points
- Concurrent Points
- Coplanar Points
- Non-coplanar Points
- Equidistant Points

Collinear Points

The word ‘collinear point’ derived from the word ‘col’ (together) and ‘linear’ (straight line) which means the points which are occurring together in a linear way.

**For Example.** There are four points D, E, F, G, occurring on a same straight line.

#### Real-life Examples.

For better understanding, the real-life examples of collinear points are numbers on a ruler, birds sitting in a row on a wire etc.

### Non-collinear Points

In contrast to the above type, non-collinear points are those which are not occurring together on a straight line. It can also be understood with the concept; as if a straight line cannot be drawn through a few points, then points are non-collinear in nature.

**For Example.** There are four points D, E, F, G, not occurring on a same straight line.

#### Real-life Examples.

For better understanding, the real-life examples of non-collinear points are sprinklers on a cake, coffee beans in a jar i.e., scattered positions of points.

### Concurrent Points

A concurrent point is that point on which two or more lines are intersected.

**For Example.** Consider the points, D, E, F, and G, making line DE and FG, such that these intersect at point H. Then the point H is known as point of intersection or concurrent point.

#### Real-life Examples.

For better understanding, the real-life examples of concurrent points are intersecting points of a kite, spider web, spokes of bicycle etc.

### Coplanar Points

The word ‘coplanar’ is derived from the word ‘co’ and ‘plane’ which means, the points which lie on the single plane. In geometry, a plane is known as a 2-D flat surface which extends indefinitely, on which a point, line and three dimensions can lie. In real life, a wall or a piece of paper are the examples of plane.

- There should be at least three points on a plane to be called as coplanar.

**For Example.** There are four points, D, E, F and G lying on a common plane.

#### Real-life Examples.

For better understanding, the real-life examples of coplanar points are the hands-on of clock, objects on a table, grids of a graph paper all lie on a single plane.

### Non-coplanar Points

Unlike coplanar points, the non-coplanar points are those which do not lie on the same plane. There should be at least four or more points which could be called as non-planar only if these are not lying on a single plane. Usually non-coplanar points exist in case of three-dimensional figures.

**For Example.** There are four points, D, E, and F lying on a common plane, However, the point is said to be non-coplanar as it does not lie on a single plane with others.

*R*eal-life Examples.

*R*

For better understanding, the real-life example is the point G on a wall with plane A would be non-coplanar to the points E and F on a wall with plane B.

### Equidistant Points

A point is said to be equidistant from others if it is at similar distance from other points.

**For Example. **The points E in the given triangle is known as equidistant point which is at similar distance from F and G respectively.

#### Real-life Example.

For better understanding, the real-life example of equidistant point is the central point of a sky wheel is equidistant from all other points.