RS Aggarwal Solutions: Line Segment, Ray and Line | Mathematics (Maths) Class 6 PDF Download

 Page 1


EXERCISE 11 (A)
Q.1. Name all the line segments in each of the
following figures :
Y
Z
X
 
A
C B
D E
(i)                     (ii)
P Q R S
(iii)
Sol. Line segment
(i) In figure (i) are 
XY
 and 
YZ
(ii) In figure (ii) 
AD
, 
AB
, AC, 
AE
, 
BD
,
BC , CE
(iii) In figure (iii) PQ , 
PR
, PS , QR , QS
and RS
Q. 2. Identify and name the line segments and
rays in each of the following figures :
Sol. (i) In fig. (i), line segments is AB, and
rays are AC and BD .
(ii) In fig. (ii), line segments are
GE GP EP , , and rays are
EF GH PQ , , .
(iii) In fig. (iii), line segments are 
OL OP ,
and rays are LM PQ , .
Q. 3. In the adjoining figure, name
(i) four line segments ;
(ii) four rays ;
(iii) two non-intersecting line segments.
Sol. (i) Four line segments are PR QR PQ , ,
and RS.
(ii) Four ray can be 
PA QC RB SD , , ,
(iii) PR and QS are two non-intersecting
lines.
Q. 4. What do you mean by collinear points ?
Page 2


EXERCISE 11 (A)
Q.1. Name all the line segments in each of the
following figures :
Y
Z
X
 
A
C B
D E
(i)                     (ii)
P Q R S
(iii)
Sol. Line segment
(i) In figure (i) are 
XY
 and 
YZ
(ii) In figure (ii) 
AD
, 
AB
, AC, 
AE
, 
BD
,
BC , CE
(iii) In figure (iii) PQ , 
PR
, PS , QR , QS
and RS
Q. 2. Identify and name the line segments and
rays in each of the following figures :
Sol. (i) In fig. (i), line segments is AB, and
rays are AC and BD .
(ii) In fig. (ii), line segments are
GE GP EP , , and rays are
EF GH PQ , , .
(iii) In fig. (iii), line segments are 
OL OP ,
and rays are LM PQ , .
Q. 3. In the adjoining figure, name
(i) four line segments ;
(ii) four rays ;
(iii) two non-intersecting line segments.
Sol. (i) Four line segments are PR QR PQ , ,
and RS.
(ii) Four ray can be 
PA QC RB SD , , ,
(iii) PR and QS are two non-intersecting
lines.
Q. 4. What do you mean by collinear points ?
(i) How many lines can you draw
passing through three collinear points ?
(ii) Given three collinear points A, B, C.
How many lines segments do they
determine ? Name them.
Sol. (i) Three or more points in a plane are said
to be collinear if they all lie on the same
line.
(ii) In the figure given above, points A, B,
C are collinear points.
We can draw exactly one line passing
through three collinear points.
Q. 5. In the adjoining figure name :
(i) Four pairs of intersectong lines.
(ii) Four collinear points
(iii) Three non-collinear points
(iv) Three concurrent lines
(v) Three lines whose point of intersection
is P.
Sol. (i) Four pairs of intersecting lines are :
(AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS)
(ii) Four collinear points are :  A, Q, S, B
(iii) Three non-collinear points are : A, Q, P
(iv) Three concurrent lines are : AB, PS and
RS.
(v) Three lines whose point of intersecton
is P are : CD, PQ and PS.
Q. 6. Mark three non-collinear points A, B, C
as shown. Draw lines through these
points taking two at a time. Name the
lines.
How many such different lines can be
drawn.
Sol. The lines drawn through given points
A, B, C are as shown below. The names
of these lines are AB, BC and AC.
A B
C
Also it is clear that three different lines
can be drawn.
Q. 7. Count the number of line segments in
each of the following figures and name
them :
C
Page 3


EXERCISE 11 (A)
Q.1. Name all the line segments in each of the
following figures :
Y
Z
X
 
A
C B
D E
(i)                     (ii)
P Q R S
(iii)
Sol. Line segment
(i) In figure (i) are 
XY
 and 
YZ
(ii) In figure (ii) 
AD
, 
AB
, AC, 
AE
, 
BD
,
BC , CE
(iii) In figure (iii) PQ , 
PR
, PS , QR , QS
and RS
Q. 2. Identify and name the line segments and
rays in each of the following figures :
Sol. (i) In fig. (i), line segments is AB, and
rays are AC and BD .
(ii) In fig. (ii), line segments are
GE GP EP , , and rays are
EF GH PQ , , .
(iii) In fig. (iii), line segments are 
OL OP ,
and rays are LM PQ , .
Q. 3. In the adjoining figure, name
(i) four line segments ;
(ii) four rays ;
(iii) two non-intersecting line segments.
Sol. (i) Four line segments are PR QR PQ , ,
and RS.
(ii) Four ray can be 
PA QC RB SD , , ,
(iii) PR and QS are two non-intersecting
lines.
Q. 4. What do you mean by collinear points ?
(i) How many lines can you draw
passing through three collinear points ?
(ii) Given three collinear points A, B, C.
How many lines segments do they
determine ? Name them.
Sol. (i) Three or more points in a plane are said
to be collinear if they all lie on the same
line.
(ii) In the figure given above, points A, B,
C are collinear points.
We can draw exactly one line passing
through three collinear points.
Q. 5. In the adjoining figure name :
(i) Four pairs of intersectong lines.
(ii) Four collinear points
(iii) Three non-collinear points
(iv) Three concurrent lines
(v) Three lines whose point of intersection
is P.
Sol. (i) Four pairs of intersecting lines are :
(AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS)
(ii) Four collinear points are :  A, Q, S, B
(iii) Three non-collinear points are : A, Q, P
(iv) Three concurrent lines are : AB, PS and
RS.
(v) Three lines whose point of intersecton
is P are : CD, PQ and PS.
Q. 6. Mark three non-collinear points A, B, C
as shown. Draw lines through these
points taking two at a time. Name the
lines.
How many such different lines can be
drawn.
Sol. The lines drawn through given points
A, B, C are as shown below. The names
of these lines are AB, BC and AC.
A B
C
Also it is clear that three different lines
can be drawn.
Q. 7. Count the number of line segments in
each of the following figures and name
them :
C
Sol. (i) In the the given figure, there are six
line segments, namely AB, AC, AD, BD,
BC, DC.
(ii) In the given figure, there are ten line
segments, namely, AD, AB, AC, AO,
OC, BC, BD, BO, OD, CD.
(iii) In the given figure, there are six line
segments, namely AB, AF, BF, CD, DE,
CE.
(iv) In the given figure, there are twelve line
segments, namely, AB, BC, CD, AD, BF,
CG, DH, AE, EF, FG, GH, EH.
Q.8. Consider the line 
PQ
 given below and
find whether the given statements are true
or false :
P L M N Q
(i) M is a point on ray 
NQ
.
(ii) L is a point on ray 
MP
.
(iii) Ray 
MQ
 is different from ray 
NQ
.
(iv) L, M, N are points on line segment 
LN
.
(v) Ray LP is different from ray LQ .
Sol.
PQ
 is a line
P L M N Q
(i) False, as M does not lie on 
NQ
(ii) True (iii) True
(iv) True (v) True
Q. 9. Write ‘T’ for true and ‘F’ for false in
case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray AB is the same as the ray 
BA .
(v) The line segment AB is the same as the
line segment BA.
(vi) The line AB is the same as the line BA .
(vii) Two points A and B in a plane determine
a unique line segment.
(viii) Two intersecting lines intersect at a point.
(ix) Two intersecting planes intersect at a
point.
(x) If points A, B, C are collinear and points
Page 4


EXERCISE 11 (A)
Q.1. Name all the line segments in each of the
following figures :
Y
Z
X
 
A
C B
D E
(i)                     (ii)
P Q R S
(iii)
Sol. Line segment
(i) In figure (i) are 
XY
 and 
YZ
(ii) In figure (ii) 
AD
, 
AB
, AC, 
AE
, 
BD
,
BC , CE
(iii) In figure (iii) PQ , 
PR
, PS , QR , QS
and RS
Q. 2. Identify and name the line segments and
rays in each of the following figures :
Sol. (i) In fig. (i), line segments is AB, and
rays are AC and BD .
(ii) In fig. (ii), line segments are
GE GP EP , , and rays are
EF GH PQ , , .
(iii) In fig. (iii), line segments are 
OL OP ,
and rays are LM PQ , .
Q. 3. In the adjoining figure, name
(i) four line segments ;
(ii) four rays ;
(iii) two non-intersecting line segments.
Sol. (i) Four line segments are PR QR PQ , ,
and RS.
(ii) Four ray can be 
PA QC RB SD , , ,
(iii) PR and QS are two non-intersecting
lines.
Q. 4. What do you mean by collinear points ?
(i) How many lines can you draw
passing through three collinear points ?
(ii) Given three collinear points A, B, C.
How many lines segments do they
determine ? Name them.
Sol. (i) Three or more points in a plane are said
to be collinear if they all lie on the same
line.
(ii) In the figure given above, points A, B,
C are collinear points.
We can draw exactly one line passing
through three collinear points.
Q. 5. In the adjoining figure name :
(i) Four pairs of intersectong lines.
(ii) Four collinear points
(iii) Three non-collinear points
(iv) Three concurrent lines
(v) Three lines whose point of intersection
is P.
Sol. (i) Four pairs of intersecting lines are :
(AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS)
(ii) Four collinear points are :  A, Q, S, B
(iii) Three non-collinear points are : A, Q, P
(iv) Three concurrent lines are : AB, PS and
RS.
(v) Three lines whose point of intersecton
is P are : CD, PQ and PS.
Q. 6. Mark three non-collinear points A, B, C
as shown. Draw lines through these
points taking two at a time. Name the
lines.
How many such different lines can be
drawn.
Sol. The lines drawn through given points
A, B, C are as shown below. The names
of these lines are AB, BC and AC.
A B
C
Also it is clear that three different lines
can be drawn.
Q. 7. Count the number of line segments in
each of the following figures and name
them :
C
Sol. (i) In the the given figure, there are six
line segments, namely AB, AC, AD, BD,
BC, DC.
(ii) In the given figure, there are ten line
segments, namely, AD, AB, AC, AO,
OC, BC, BD, BO, OD, CD.
(iii) In the given figure, there are six line
segments, namely AB, AF, BF, CD, DE,
CE.
(iv) In the given figure, there are twelve line
segments, namely, AB, BC, CD, AD, BF,
CG, DH, AE, EF, FG, GH, EH.
Q.8. Consider the line 
PQ
 given below and
find whether the given statements are true
or false :
P L M N Q
(i) M is a point on ray 
NQ
.
(ii) L is a point on ray 
MP
.
(iii) Ray 
MQ
 is different from ray 
NQ
.
(iv) L, M, N are points on line segment 
LN
.
(v) Ray LP is different from ray LQ .
Sol.
PQ
 is a line
P L M N Q
(i) False, as M does not lie on 
NQ
(ii) True (iii) True
(iv) True (v) True
Q. 9. Write ‘T’ for true and ‘F’ for false in
case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray AB is the same as the ray 
BA .
(v) The line segment AB is the same as the
line segment BA.
(vi) The line AB is the same as the line BA .
(vii) Two points A and B in a plane determine
a unique line segment.
(viii) Two intersecting lines intersect at a point.
(ix) Two intersecting planes intersect at a
point.
(x) If points A, B, C are collinear and points
C, D, E are collinear then the points A, B,
C, D, E are collinear.
(xi) One and only one ray can be drawn with
a given end point.
(xii) One and only one line can be drawn to
pass through two given points.
(xiii) An unlimited number of lines can be
drawn to pass through a given point.
Sol. (i) False
.
.
.
Point has no dimensions.
(ii) False
.
.
.
 A line segment has a length.
(iii) False
.
.
.
 A ray has no finite length.
(iv) False
.
.
.
If AB and ray 
BA
 have opposite
directions.
(v) True
.
.
.
 Length of AB and BA is same.
(vi) True
.
.
.
 Line AB and BA are same.
(vii) True
.
.
.
 Distance between A and B or B and A is same,
so they determine a unique line segment.
(viii) True
.
.
.
 Two lines intersect each other at one point.
(ix) False
.
.
.
    Two intersecting planes intersect at one line
not at one point.
(x) False
.
.
.
     If A, B, C are collinear and points C, D, E
are collinear then it is not necessary that there
points A, B, C, D and E are collinear.
(xi) False
.
.
.
     Infinite number of rays can be drawn with a
given end point.
(xii) True
.
.
. 
   We can draw one and only one line passing
through two given points.
(xiii) True
.
.
.
We can draw infinite number of lines pass
through a given point.
Q. 10. Fill in the blanks :
(i) A line segment has a ............ length.
(ii) A ray has ............ end point.
(iii) A line has ............ end point.
(iv) A ray has no ............ length.
(v) A line ............ be drawn on a paper.
Sol. (i) definite (ii) one        (iii) no
(iv) definite (v) cannot. Ans.
EXERCISE 11 (B)
Mark ( ) against the correct answer
in each of following.
Q. 1. Which of the following has no end
points ?
(a) a line segment (b) a ray
(c) a line (d) none of these
Sol. (c) a line has no end points
Q. 2. Which of the following has one end
point ?
(a) a line (b) a ray
(c) a line segment (d) none of these
Sol. (b) a ray has no end points
Q. 3. Which of the following has two end
points ?
(a) a line segment (b) a ray
(c) a line (d) none of these
Sol. (a) a line segment has two end points
Q. 4. Which of the following has definite
length ?
(a) a line (b) a line segment
(c) a ray (d) none of these
Sol. (b) a line segment has definite length
Q. 5. Which of the following can be drawn on
a piece of paper ?
(a) a line (b) a line segment
(c) a ray (d) a plane
Sol. (b) a line segment can be drawn on a
piece of paper
Q. 6. How many lines can be drawn passing
through a given point ?
Page 5


EXERCISE 11 (A)
Q.1. Name all the line segments in each of the
following figures :
Y
Z
X
 
A
C B
D E
(i)                     (ii)
P Q R S
(iii)
Sol. Line segment
(i) In figure (i) are 
XY
 and 
YZ
(ii) In figure (ii) 
AD
, 
AB
, AC, 
AE
, 
BD
,
BC , CE
(iii) In figure (iii) PQ , 
PR
, PS , QR , QS
and RS
Q. 2. Identify and name the line segments and
rays in each of the following figures :
Sol. (i) In fig. (i), line segments is AB, and
rays are AC and BD .
(ii) In fig. (ii), line segments are
GE GP EP , , and rays are
EF GH PQ , , .
(iii) In fig. (iii), line segments are 
OL OP ,
and rays are LM PQ , .
Q. 3. In the adjoining figure, name
(i) four line segments ;
(ii) four rays ;
(iii) two non-intersecting line segments.
Sol. (i) Four line segments are PR QR PQ , ,
and RS.
(ii) Four ray can be 
PA QC RB SD , , ,
(iii) PR and QS are two non-intersecting
lines.
Q. 4. What do you mean by collinear points ?
(i) How many lines can you draw
passing through three collinear points ?
(ii) Given three collinear points A, B, C.
How many lines segments do they
determine ? Name them.
Sol. (i) Three or more points in a plane are said
to be collinear if they all lie on the same
line.
(ii) In the figure given above, points A, B,
C are collinear points.
We can draw exactly one line passing
through three collinear points.
Q. 5. In the adjoining figure name :
(i) Four pairs of intersectong lines.
(ii) Four collinear points
(iii) Three non-collinear points
(iv) Three concurrent lines
(v) Three lines whose point of intersection
is P.
Sol. (i) Four pairs of intersecting lines are :
(AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS)
(ii) Four collinear points are :  A, Q, S, B
(iii) Three non-collinear points are : A, Q, P
(iv) Three concurrent lines are : AB, PS and
RS.
(v) Three lines whose point of intersecton
is P are : CD, PQ and PS.
Q. 6. Mark three non-collinear points A, B, C
as shown. Draw lines through these
points taking two at a time. Name the
lines.
How many such different lines can be
drawn.
Sol. The lines drawn through given points
A, B, C are as shown below. The names
of these lines are AB, BC and AC.
A B
C
Also it is clear that three different lines
can be drawn.
Q. 7. Count the number of line segments in
each of the following figures and name
them :
C
Sol. (i) In the the given figure, there are six
line segments, namely AB, AC, AD, BD,
BC, DC.
(ii) In the given figure, there are ten line
segments, namely, AD, AB, AC, AO,
OC, BC, BD, BO, OD, CD.
(iii) In the given figure, there are six line
segments, namely AB, AF, BF, CD, DE,
CE.
(iv) In the given figure, there are twelve line
segments, namely, AB, BC, CD, AD, BF,
CG, DH, AE, EF, FG, GH, EH.
Q.8. Consider the line 
PQ
 given below and
find whether the given statements are true
or false :
P L M N Q
(i) M is a point on ray 
NQ
.
(ii) L is a point on ray 
MP
.
(iii) Ray 
MQ
 is different from ray 
NQ
.
(iv) L, M, N are points on line segment 
LN
.
(v) Ray LP is different from ray LQ .
Sol.
PQ
 is a line
P L M N Q
(i) False, as M does not lie on 
NQ
(ii) True (iii) True
(iv) True (v) True
Q. 9. Write ‘T’ for true and ‘F’ for false in
case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray AB is the same as the ray 
BA .
(v) The line segment AB is the same as the
line segment BA.
(vi) The line AB is the same as the line BA .
(vii) Two points A and B in a plane determine
a unique line segment.
(viii) Two intersecting lines intersect at a point.
(ix) Two intersecting planes intersect at a
point.
(x) If points A, B, C are collinear and points
C, D, E are collinear then the points A, B,
C, D, E are collinear.
(xi) One and only one ray can be drawn with
a given end point.
(xii) One and only one line can be drawn to
pass through two given points.
(xiii) An unlimited number of lines can be
drawn to pass through a given point.
Sol. (i) False
.
.
.
Point has no dimensions.
(ii) False
.
.
.
 A line segment has a length.
(iii) False
.
.
.
 A ray has no finite length.
(iv) False
.
.
.
If AB and ray 
BA
 have opposite
directions.
(v) True
.
.
.
 Length of AB and BA is same.
(vi) True
.
.
.
 Line AB and BA are same.
(vii) True
.
.
.
 Distance between A and B or B and A is same,
so they determine a unique line segment.
(viii) True
.
.
.
 Two lines intersect each other at one point.
(ix) False
.
.
.
    Two intersecting planes intersect at one line
not at one point.
(x) False
.
.
.
     If A, B, C are collinear and points C, D, E
are collinear then it is not necessary that there
points A, B, C, D and E are collinear.
(xi) False
.
.
.
     Infinite number of rays can be drawn with a
given end point.
(xii) True
.
.
. 
   We can draw one and only one line passing
through two given points.
(xiii) True
.
.
.
We can draw infinite number of lines pass
through a given point.
Q. 10. Fill in the blanks :
(i) A line segment has a ............ length.
(ii) A ray has ............ end point.
(iii) A line has ............ end point.
(iv) A ray has no ............ length.
(v) A line ............ be drawn on a paper.
Sol. (i) definite (ii) one        (iii) no
(iv) definite (v) cannot. Ans.
EXERCISE 11 (B)
Mark ( ) against the correct answer
in each of following.
Q. 1. Which of the following has no end
points ?
(a) a line segment (b) a ray
(c) a line (d) none of these
Sol. (c) a line has no end points
Q. 2. Which of the following has one end
point ?
(a) a line (b) a ray
(c) a line segment (d) none of these
Sol. (b) a ray has no end points
Q. 3. Which of the following has two end
points ?
(a) a line segment (b) a ray
(c) a line (d) none of these
Sol. (a) a line segment has two end points
Q. 4. Which of the following has definite
length ?
(a) a line (b) a line segment
(c) a ray (d) none of these
Sol. (b) a line segment has definite length
Q. 5. Which of the following can be drawn on
a piece of paper ?
(a) a line (b) a line segment
(c) a ray (d) a plane
Sol. (b) a line segment can be drawn on a
piece of paper
Q. 6. How many lines can be drawn passing
through a given point ?
(a) one only (b) two
(c) three (d) unlimited number
Sol. (d) unlimited number can be drawn
passing through a given point
Q. 7. How many lines can be drawn passing
through two given points ?
(a) one only (b) two
(c) three (d) unlimited number
Sol. (a) one only can be drawn passing
through two given points
1. (c) 
.
.
.
 A line has no end points.
2. (b) 
.
.
.
 A ray his one end point.
3. (a) 
.
.
.
 A line segment has two end points.
4. (b) 
.
.
.
 A line segment has definite length.
5. (b) 
.
.
.
 A line segment can be drawn on a
piece of paper.
6. (d) 
.
.
.
 Unlimited number of lines can be
draw passing through a given point.
7. (a) 
.
.
.
 One and only one line can be drawn
passing through two given points.
Q.8. Two planes intersect
(a) at a point (b) in a plane
(c) in a line (d) none of these
Sol. Two planes intersect in a line. (c)
Q.9. Two lines intersect
(a) at a point (b) at two points
(c) at an infinite number of points
(d) in a line
Sol. Two lines intersect at a point. (a)
Q.10. Two points in a plane determine
(a) exactly one line segment
(b) exactly two line segments
(c) an infinite number of line segments
(d) none of these
Sol. Two points in a plane determine exactly
one line segment. (a)
Q.11. The minimum number of points of
intersection of three lines in a plane is
(a) 1 (b) 2
(c) 3 (d) 0
Sol. The minimum number of points of
intersection of three lines in a plane is 0.
(d)
Q.12. The maximum number of points of
intersection of three lines in a plane is
(a) 0 (b) 1
(c) 2 (d) 3
Sol. The maximum number of a points of
intersection of three lines in a plane is 3
(d)
Q.13. Choose the correct statement :
(a) every line has a definite length
(b) every ray has a definite length
(c) every line segment has a definite length
(d) none of these
Sol. Every line segment has a definite length.
(c)
Q.14. Choose the false statement :
(a) Line 
AB
 is the same as line 
BA
(b) Ray 
AB
 is the same as ray 
BA
(c) Line segment 
AB
 is the same as the line
segment 
BA
(d) none of these
Sol. Ray  
AB
 is not same as ray 
BA
Both are different. Hence 
AB
 is same
as 
BA
 is false. (b)
Q.15. How many rays can be drawn with a
given point as the initial point ?
(a) One (b) Two
(c) An unlimited number
(d) A limited number only
Sol. An unlimited number of rays can be
drawn with a given point as the initial
point. (c)