Library Home CBSE - VI (Change Class)

Select subject
Points, Lines and Curves

Points, Lines and Curves

The most practical branch of mathematics is geometry.  The term 'geometry' is derived from the Greek word 'geometron'.

Lesson Demo

The most practical branch of mathematics is geometry.  The term 'geometry' is derived from the Greek word 'geometron'.  It means Earth's measurement.  The fundamental elements of geometry are given below:

Point:

In geometry, dots are used to represent points. A point is used to represent any specific location or position.  It neither has any size, nor dimensions such as length or breadth.  A point can be denoted by a capital letter of the English alphabet.   Points can be joined in different ways.

Line segment:

A line segment is defined as the shortest distance between two points.  For example, if we mark any two points, M and N, on a sheet of paper, then the shortest way to join M to N is a line segment.  It is denoted by   Points M and N are called the end points of the line segment.

Line:

A line is made up of an infinite number of points that extend indefinitely in either direction.  For example, if a line segment from M to N is extended beyond M in one direction and beyond N in the other, then we get a line, MN.  It is denoted by   A line can also be represented by small letters of the English alphabet.

Ray:

A ray is a portion of a line.  It starts at one point and goes on endlessly in one direction.    For example, if a line from M to N is extended endlessly in the direction of N, then we get a ray, MN.  It is denoted by   and can be read as ray MN.

Plane:

A plane is said to be a very thin flat surface that
does not have any thickness, and is limitless.  For
example, this sheet  is said to plane PQR.  An infinite
number of points can be contained within a plane.

Intersecting lines:

If two lines pass through a point, then we say that the two lines intersect at that point.  Thus, if two lines have one point in common, then they are called intersecting lines.  For example, two lines
pass though point P.  These two lines are called intersecting lines.

Parallel lines or non- intersecting lines :

In a plane, if two lines have no point in common, then they are said to be parallel or non- intersecting lines.
Parallel lines never meet, cut or cross each other.  In the figure, it can be observed that two lines  are parallel.  We write .

Curves:

Curves can be defined as figures that flow smoothly without a break.  A line is also a curve, and is called a straight curve.  Curves that do not intersect themselves are called simple curves. The end points join to enclose an area. Such curves are called closed curves.  For example, (i), (ii) and (iii) are simple curves, whereas (iv) and (v) are closed curves.

For a closed curve, we can identify three regions:

• The interior of the curve.  Here, point P is in the interior of the circle.
• Boundary of the curve.  Here, point P is on the circle.
• Exterior of the curve.  Here, point P is in the exterior of the circle.