Points and Lines

Geometry is a branch of mathematics that deals with drawing various shapes and figures. Before studying geometry, there are some important terms and concepts you need to be familiar with. 

Drawing any figure or a shape always starts off from a point. From a point, we start drawing a line and construct various shapes and patterns. 

In this mini-lesson we will learn the properties of a point, definitions of a point and a line, how to different types of lines with solved examples and interactive questions.

Introduction to points and lines

Lesson Plan

What Is a Point?

Definition of a Point

A point is defined as a location in any space. It is represented by a (.)

Point diagram

Properties of a Point

  • A point does not have any length, height, shape, size.
  • It marks the beginning to draw any figure or shape.
  • A marked point is labelled by a capital letters

Let us discuss the types of points. 

Collinear Points and Non-Collinear Points

Collinear points

If there are three or more points on the same line then they are called collinear points. Here all the points lie on the same line. A,B and C are collinear points.

If there are a group of points that do not lie on the same line then they are called  non-collinear points. D and E are non-collinear points.

Coplanar Points and Non-Coplanar Points

Coplanar and non-coplanar

If a group of points lie on the same plane then they are said to be coplanar points. A plane is a two-dimensional flat surface that extends infinitely.

A set of points that do not lie on the same plane are non-coplanar points.

Definition of a Line

A series of points connected by a straight path is defined as a line.

A line

Properties of a Line

  • A line is usually defined by two points marked in capital letters
  • It extends indefinitely in both the directions
  • Length of a line is undefined
  • It is denoted by the following notatation \(\begin{align}\overrightarrow{AB}\end{align}\)
  • There are infinite number of points on a line

Now let us discuss the types of lines.

Horizontal Line

A line that moves from left to right is called a horizonal line.

Horizontal line

Vertical Line

A line that moves from top to bottom is called a vertical line.

Vertical line

Parallel Line

Two lines are said to be parallel if they do not meet and intersect at any point. The two lines below are said to be parallel lines.

Parallel lines

Perpendicular Line

Two lines are said to be perpendicular if they meet or intersect exactly at 900.

Perpendicular line

Intersecting Line

Two lines are said to intersect if they meet at a point.

Intersecting lines


Examples of Points and Lines in Real-World

Real world examples for point and lines

important notes to remember
Important Notes
  1. A point does not have a defined length, width and size
  2. When two distinct points are connected we get a line. 
  3. A line extends in both the directions infinitely. A line segment is a part of a line and has a definite measure.
  4. Parallel lines do not intersect each other.
  5. The lines that intersect each other at 900 are called perpendicular lines.

Solved Examples

Example 1

 

 

Which of the following are collinear points and non-collinear points?

Example 1 for points

Solution

The points A,B,C lie on the same line and they are collinear points.

The point D and E do not lie on the same line and so they are non-collinear points.

Points A,B,C are collinear.
Points D and E are non-collinear.

Example 2

 

 

Find the set of coplanar and non-coplanar points from the figure.

coplanar and non-coplanar

Solution

Points A,B and C lie on the same plane and so they are coplanar points.

Points A,B,C and D are non-coplanar since point D lies outside the plane.

A,B,C are coplanar points.
A,B,C and D are non-coplanar points.

Example 3

 

 

Draw a figure to find the point of intersection of the three lines AB and CD and EF.

Solution

Example 3 question on point of intersection

The lines AB and CD and EF intersect at the point X.
Example 4

 

 

Find and label all types of lines from the figure given below.

Example 4 question

Solution

AB and CD are horizontal lines since they move from left to right.
XY is a vertical line since it moves from top to bottom.
AB and CD are parallel lines since they do not meet and intersect at any point.
Lines XY and AB intersect at point O.
Line XY is perpendicular to AB since the lines make 900 with each other.

AB and CD are horizontal lines.
XY is a vertical line.
AB and CD are parallel lines.
Lines XY and AB intersect at point O.
XY is perpendicular to AB.

 
tips and tricks
Tips and Tricks
  1. Two distinct points are required to draw a line.
  2. Two points are always said to be collinear.
  3. Any three points in a plane are said to be coplanar but not necessarily collinear, since they may or may not lie on the same row.

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 

Let's Summarize

The lesson targeted the fascinating concept of points and lines. The math journey around points and lines starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


FAQs on Points and Lines

1. Why are points, lines and planes important?

The concepts of lines, points and planes are important as they form the base to understand the concepts of geometry. 

2. How many points are contained in a line?

There are two points in a line. The point at which the line starts and the point at which it ends are the two points.

3. Why are points is enough to fix lines?

Two points are enough to fix a line.

4. What are the names of types of lines?

Horizontal,vertical,parallel and perpendicular are the types of lines.

5. How many end points are there in a line?

A line does not have a end point as it extends infinitely in both the directions.

6. What are points on the same plane called?

Lines on the same plane are called coplanar lines.

7. Is line AB the same as BA?

Yes the lines AB and BA are the same because they both pass through the same points A and B.

8. What is the set of all points?

Set of all points  is called a locus.

9. What are the types of lines?

Horizontal,vertical,parallel and perpendicular are the types of lines.

10. How to represent any point?

A point is represented using a (.). It is marked using a capital letter like A,B. It is read a "point A".

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