Point in Geometry Math | Collinear Points and non-collinear points Examples

This article explained defections of points in geometry math, Collinear Points, and Non-collinear points with examples.

Table of Contents

Point in Math | Collinear Points | Non-collinear points | All Math Tricks

The terms Point, Line, Plane and space .. etc are fundamental concepts in study of geometry and they

Definition of Point in Math:

A point is that which has no part. It has only one position. It does not have dimensions like length, breadth or height

Consider the step from points to solid

Point – Line – Surface – Solids

how to find collinear points | Examples of collinear points | point in geometry math | Number of Lines through non- collinear points | All math tricks

In the above figures, the first figure is Point. It has no dimension. If it further add one dimension length then it will be line segment (Line). If further add one more dimension breadth then it will have two dimension which is rectangle(Surface) . Now add one more dimension height then it has three dimension which is cuboid (Solid).

Collinear Points & non-collinear points:

Collinear points : Three or more points lying on the same line are called collinear points.

Non-collinear points : Three or more points not lying on the same line are called non-collinear points.

Examples

Let us consider three points P, Q and R in a plane. If we draw a line ” l “ passing through two points P & Q , then there are two possibilities

a) Point R lies on the line “ l “

b) Point R does not lie on the line “ l “

how to find collinear points | Examples of collinear points | point in geometry math | Number of Lines through non- collinear points | All math tricks

If a point R lies on the line “ l “ then points P , Q & R lie on the same line and are said to be collinear points.

how to find collinear points | Examples of collinear points | point in geometry math | Number of Lines through non- collinear points | All math tricks

If a point R does not lie on the line “ l “ , then points P, Q, and R do not lie on the same line and are said to be non- collinear points.

Lines through non- collinear points

Examples of non-collinear points

Let’s consider P, Q and R are non- collinear points then

how to find collinear points | Examples of collinear points | point in geometry math | Number of Lines through non- collinear points | All math tricks

Number of lines through P, Q and R non-collinear points = 3

( $\underset{PQ}{\leftrightarrow}$ , $\underset{QR}{\leftrightarrow}$ , $\underset{PR}{\leftrightarrow}$ , )

Let’s consider P, Q, R & S are non- collinear points then

how to find collinear points | Examples of collinear points | point in geometry math | Number of Lines through non- collinear points | All math tricks

Number of lines through P, Q , R & S non-collinear points

= 6 ( $\underset{PQ}{\leftrightarrow}$ , $\underset{PS}{\leftrightarrow}$ , $\underset{PR}{\leftrightarrow}$ , $\underset{QS}{\leftrightarrow}$ , $\underset{QR}{\leftrightarrow}$ , $\underset{SR}{\leftrightarrow}$

Number of lines through “n” non-collinear points = $\frac{n (n-1)}{2}$

Related Topics

Two dimensional shapes formulas.

Quadrilateral Properties | Trapezium, parallelogram, Rhombus

Types of Triangles With examples | Properties of Triangle

Properties of the circle in math | Arc, Perimeter, Segment of circle

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