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Lesson Posted on 04 Mar CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Complex Numbers and Quadratic Equations CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Linear Inequalities Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Foundation Course +2 Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Mains Coaching Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Integrated Coaching less

Sign of a quadratic polynomial Part 1

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 03 Mar CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Linear Inequalities Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Foundation Course Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Mains Coaching

Inequalities basics part 2

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 03 Mar CBSE/Class 11 CBSE/Class 11/Science/Mathematics/Unit-II: Algebra/Linear Inequalities Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Foundation Course

Inequalities basics part 3

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 03 Mar CBSE/Class 11 CBSE/Class 11/Science/Physics/Unit 2-Kinematics/Chapter 4-Motion in a Plane Exam Coaching/NEET-UG Coaching +1 Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Foundation Course less

Equality of Vectors

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 02 Mar Exam Coaching/NEET-UG Coaching Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Mains Coaching

NEET 2020 Physics Solutions Code E1 Q136 - Q140

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 02 Mar Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Mains Coaching CBSE

JEE main (24-2-2021 M ) Mathematics solutions Q 61 - Q64

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

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Lesson Posted on 27 Feb Exam Coaching/NEET-UG Coaching CBSE/Class 11/Science/Physics Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching

NEET 2018 Solutions

Rajan Mittal

I am an Engineer by qualification and a teacher by profession. I have been teaching since 1995. I teach...

This video gives explanatory solution to NEET 2018 Q.1 For physics section
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Answered on 19 Apr Exam Coaching/Engineering Entrance Coaching

Rahul P Sah

4 years of teaching experience in math physics and computer application

You can enter into the field of data science or data analyst, AI and ML, and earn a handsome package. Also, python is a trending language, so that you can get community support for at least the upcoming two decades.
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Answered on 27 Mar Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching

Priyanka Rana

IITian Mathematics Teacher with 4 years of experience

There is absolutely no problem if you join Coaching for the IIT JEE exam, but you should try a few sample question papers of FIITJEE and Akash entrance exams before that. That will give you a hint of what is the difficulty level and will increase your interest in the subjects as well.
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Lesson Posted on 24/06/2017 Exam Coaching/Foreign Education Exam Coaching/GRE Coaching Exam Coaching/Foreign Education Exam Coaching/GMAT Coaching Exam Coaching/Foreign Education Exam Coaching/SAT Coaching +2 Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching Exam Coaching/Engineering Entrance Coaching/IIT JEE Coaching/IIT JEE Advanced Coaching less

How To Determine If Points Are Collinear In Coordinate Geometry?

Ravi kota

I am a Pro-active, responsible and result-oriented Math trainer with a strong passion for student improvement...

How to prove if points are Collinear in coordinate geometry? Collinear points definition: Three or more points that lie on a same straight line are called collinear points. Consider a straight line L in the above Cartesian coordinate plane formed by x axis and y axis. This straight line L is... read more

How to prove if points are Collinear in coordinate geometry? 

 Collinear points definition:

  • Three or more points that lie on a same straight line are called collinear points.
  • Consider a straight line L in the above Cartesian coordinate plane formed by x axis and y axis.
  • This straight line L is passing through three points A, B and C whose coordinates are (2, 4), (4, 6) and (6, 8) respectively.
  • {We may also say, alternatively, that the three points A (2, 4), B (4, 6) and C (6, 8)are lying on a same straight line L}
  • Three or more points which lie on a same straight line are called collinear points.

How to find if three points are collinear?:

  • There are two methods to find if three points are collinear.
  • One is slope formula method and the other is area of triangle method.
  • Slope formula method to find that points are collinear.
  • Three or more points are collinear, if slope of any two pairs of points is same.
  • With three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC.
  • If Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points.

Example

Show that the three points A (2, 4), B (4, 6) and C (6, 8) are collinear.

Solution:

  • If the three points A (2, 4), B (4, 6) and C (6, 8) are collinear, then
  • slopes of any two pairs of points will be equal.
  • Now, apply slope formula to find the slopes of the respective pairs of points:
  • Slope of AB = (6 – 4)/ (4 – 2) = 1,
  • Slope of BC = (8 – 6)/ (6 – 4) = 1, and
  • Slope of AC = (8 – 4) /(6 – 2) = 1
  • Since slopes of any two pairs out of three pairs of points are same, this proves that A, B and C are collinear points.
  • Area of triangle to find if three points are collinear.
  • Three points are collinear if the value of area of triangle formed by the three points is zero.
  • Apply the coordinates of the given three points in the area of triangle formula. If the result for area is zero, then the given points are said to be collinear.
  • First of all, recall the formula for area of a triangle formed by three points.

It is

                                                                 

In the formula above, the two vertical bars enclosing the variables represent a determinant.

Let us apply the coordinates of the above three points A, B and C in the determinant formula above for area of a triangle to check if the answer is zero.

Since the result for area of triangle is zero, therefore A (2, 4), B (4, 6) and C (6, 8) are collinear points.

 

 

 

 

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