Page 29 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\02_Chapter_2\Chapter_2
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

While travelling from your home to the railway station, airport, bus depot or any destination like
India Gate, Jantar Mantar, you use Google Maps which shows points with red marks.

Knowledge Desk

Euclid, is known as the father
of Geometry. His famous book
‘Elements’ has 13 volumes and
considered to have the maximum
printed edition.

Red points on map
The tiny dot gives you an idea of a point. A point marks an exact position or determines a precise
location, but it has no length, breadth or height. Suppose you mark three points on a piece of paper.
Can you distinguish between these points without naming them? For identification purposes, you
need to name them. It is denoted by the capital letters.

Types of Points

(a) Collinear and non-collinear points: The word ‘collinear’ is a combination of two Latin terms–
col and linear. ‘Col’ stands for together while ‘linear’ refers to a line. If three or more points
lie on a straight line, they are called collinear points. If the points do not lie on the same line,
they are called non-collinear points. Here A, B and C are collinear, points whereas D, E and
F are non-collinear points.

E

D
F
A B C
Collinear Points Non Collinear Points

(b) Coplanar points and non-coplanar points: Points that lie in the same plane are called coplanar
points while points, that do not lie in the same plane are non-coplanar points.

T

U
W E, U, W and R are coplanar points.
R
E T, U, W and R are non-coplanar points.
Line

A line is a collection of infinite points aligned in a straight path. It is a
one-dimensional figure extending indefinitely in both directions. In m A B
the given figure, a line is shown passing through two distinct points
A and B. The arrows on both sides indicate that the line extends infinitely in both the directions.

It is denoted by AB or line m.

27 Lines and Angles