• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • CAT Online Coaching
  • CAT Coaching in Chennai
  • Bharath’s Reading List
  • CAT Preparation
    • How to Prepare for CAT Exam
      • How to Prepare for CAT Quantitative Aptitude
      • How to prepare for CAT DILR
      • How to prepare for CAT VARC
    • 2IIM’s CAT Questions
    • CAT Syllabus
    • CAT Previous Year Paper
    • What is CAT Exam all about?
  • 2IIM CAT Preparation Reviews

2IIM CAT Preparation Blog

The Best CAT Online Coaching

Best Online CAT Coaching

  • Email
  • Facebook
  • Instagram
  • LinkedIn
  • Phone
  • YouTube
You are here: Home / CAT Quantitative Aptitude / CAT Geometry : Point, Line and a Plane

CAT Geometry : Point, Line and a Plane6 min read

June 11, 2017 By Rajesh 6 min read

A CAT Geometry question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts – Triangles, Circles, Quadrilaterals, Polygons & mixture of the above mentioned concepts. In CAT Exam, one can generally expect to get 4~6 questions from CAT Geometry. CAT Geometry is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to solve these questions one after the other, head on here. 2IIMs Question bank is absolutely free.

We are going to deal with only one question today. And behind this question, lies a very interesting idea of explaining the difference between a point, a line and a plane.

The question is as follows. You have 4 points, no three of which are collinear. How many planes can be drawn out of 3 of these points at a time?

But before we go on to the question, as we always do at 2IIM, lets start with the interesting part, the theory/concept.

We will be covering the following to answer this question;

What is a Line, Point and a plane?

  1. Number of lines through one or more points.
  2. How to find the Number of planes through one or more lines.
  3. Number of planes through two or more points.

First, lets put the image of a point, line and a plane in our heads. Take a look at the given images.

CAT Geometry Points, Lines and Plane


Number of Lines through one or more points:

Lets take a point. How many lines can be drawn through it? Infinite right? Sounds simple enough. Lets take this one step further.

CAT Geometry Number of lines through one or more points

Take two points, how many lines can be drawn through this? Only one. No matter where these points are, you can join the two points and thus create a line out of thin air.

Now take three points, you can draw a maximum of one line that goes through all of them. But there is a caveat here. This will only happen if the three points are collinear. If they are non-collinear, you cannot draw a line that passes through all of them.

With 4 points, you can still draw a line if they are collinear. Similarly, you can draw one line with ‘n’ number of points if all the points are collinear.

Number of planes through a line:

CAT Geometry Number of planes through a line

Lets take one line. How many planes can that line lie on? There can be infinite planes that this line can lie on. Look at the image below to get a clear picture.

If you are able to comprehend this, move on to the next paragraph. If not, try the following. Take a notebook. And open it to the center page. The line in the middle that segregates the notebook into right and left halves is your line. Now hold the book facing upwards. The entire notebook forms a plane, and the line segment (center line) lies on the plane. Now, you can create thousands of planes by rotating the entire notebook (as it is) clockwise or counter-clockwise. As you rotate the notebook, stop rotating the notebook at different positions. Each position you stop at is a plane. And in this plane, you will still find your line which is the center line segregating the book into 2 halves. So, the (middle line that segregates the book into two halves) line will always fall on every single plane that you create (with the notebook).

Number of planes through a point:

So, we have established that a line can lie on infinite planes. And we know that 2 points create one line. So, a line made up of 2 points can lie on infinite planes. Similarly, a line made up of 3 points(only if they are collinear) can lie on infinite planes. A line made up of ‘n’ points(if they are collinear) can lie on infinite planes.

Now, lets remove the collinearity. Lets take three points that are not collinear. You can connect these three points to form a triangle and this triangle will definitely fall on exactly one and ONLY one plane. Look at the image below to understand this.

CAT Geometry Number of planes through a point


Okay, we have gone through the entire concept of point, line and plane. Lets move on to the question.

Q. You have 4 points, no three of which are collinear. How many planes can be drawn out of 3 of these points at a time?

A. You are choosing a set of 3 points out of 4 given points. And any set of the three chosen points are non-collinear.

Irrespective of which 3 points you choose, you can draw only one plane such that all these three points lie on the plane.

So, you can choose these 3 points out of the 4 given points in 4C3 ways. So, the number of planes that lie out of 3 “non-collinear points” picked out of 4 arbitrary non-collinear points is the value of 4C3. Which is 4.

A very elaborate concept in CAT Geometry. Explained with one simple question.

Rajesh Balasubramanian takes the CAT every year and is a 4-time CAT 100 percentiler. He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.

Share this:

  • Twitter
  • Facebook
  • WhatsApp

Reader Interactions

Leave a Reply Cancel reply

Primary Sidebar

Recent Posts

  • CAT Mock Exams: Tips to Remember
  • Tips for 1st year MBA students
  • Reading List | This Week | June 4th week 2022
  • Common MBA Myths
  • Mistakes to avoid during MBA

Categories

  • Announcements (37)
  • B-School Selection Process (9)
  • CAT 2020 (33)
  • CAT 2021 (81)
  • CAT 2022 (11)
  • CAT DILR (19)
    • Data Interpretation For CAT (4)
    • Logical Reasoning For CAT (6)
  • CAT Gyan (93)
  • CAT Live Sessions (2)
    • CAT Meetup (1)
  • CAT Preparation Strategy (189)
    • Achievers talk (6)
    • Announcements (29)
  • CAT Quantitative Aptitude (30)
  • CAT Reading List (136)
    • Economy Business (1)
    • Fiction Others (1)
    • Humans Culture (2)
    • Politics Law Crime (2)
    • Psychology & Philosophy (2)
    • Reading List – This Week (125)
    • Technology Industry Science (2)
  • CAT Verbal Ability (18)
    • CAT Reading Comprehension (10)
  • CAT WAT GDPI (17)
  • GMAT (2)
  • IIFT 2022-2024 (1)
  • IPMAT (3)
  • MAH-CET Preparation (1)
  • mba (24)
    • rural management (1)
  • MICAT (1)
  • Mock CATs (5)
  • NMAT (3)
  • PGDBA Examination (2)
  • SNAP 2021 (1)
  • Top B-schools (5)
  • Uncategorized (12)
  • XAT 2021 (4)
  • XAT 2022 (2)
  • XAT Preparation (10)
    • Announcements (3)

Archives

  • June 2022 (21)
  • May 2022 (17)
  • April 2022 (9)
  • March 2022 (4)
  • February 2022 (6)
  • January 2022 (4)
  • December 2021 (1)
  • November 2021 (4)
  • October 2021 (12)
  • September 2021 (14)
  • August 2021 (32)
  • July 2021 (31)
  • June 2021 (22)
  • May 2021 (9)
  • April 2021 (5)
  • March 2021 (14)
  • February 2021 (15)
  • January 2021 (21)
  • December 2020 (19)
  • November 2020 (8)
  • October 2020 (14)
  • September 2020 (33)
  • August 2020 (31)
  • July 2020 (31)
  • June 2020 (12)
  • May 2020 (9)
  • April 2020 (8)
  • March 2020 (12)
  • February 2020 (10)
  • January 2020 (14)
  • December 2019 (5)
  • November 2019 (5)
  • October 2019 (7)
  • September 2019 (11)
  • August 2019 (6)
  • June 2017 (1)
  • October 2015 (1)
  • August 2015 (1)
  • January 2011 (1)

Follow Us!

  • Email
  • Facebook
  • Instagram
  • LinkedIn
  • Phone
  • YouTube

Footer

The heights by great men reached and kept were not attained by sudden flight,
but they, while their companions slept,
were toiling upward in the night.

- Henry Wadsworth Longfellow

Copyright © 2019. All rights reserved by 2iim.com - A Fermat Education initiative. Privacy policy | Terms & Conditions