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RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 11 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 23 - The Straight Lines.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 11 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 11 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.1

Solution 1

Solution 2

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 4

Solution 5(i)

Solution 5(ii)

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.3

Solution 1

Solution 2

y minus y subscript 1 equals m open parentheses x minus x subscript 1 close parentheses
S i n c e space t h e space l i n e space c u t s space t h e space x minus a x i s space a t space open parentheses minus 3 comma 0 close parentheses space w i t h space s l o p e space minus 2 comma space w e space h a v e comma
y minus 0 equals minus 2 open parentheses x plus 3 close parentheses
rightwards double arrow y equals minus 2 x minus 6
rightwards double arrow 2 x plus y plus 6 equals 0

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.4

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

T h e space l i n e space p a s s e s space t h r o u g h space t h e space p o i n t space open parentheses 2 comma 0 close parentheses.
A l s o space i t s space i n c l i n a t i o n space t o space y minus a x i s space i s space 135 degree.
T h a t space i s comma space t h e space i n c l i n a t i o n space o f space t h e space g i v e n space l i n e space w i t h space t h e space x minus a x i s space i s space 180 degree minus 135 degree.
T h a t space i s comma space t h e space s l o p e space o f space t h e space g i v e n space l i n e space i s space 45 degree
T h e space e q u a t i o n space o f space t h e space l i n e space h a v i n g space s l o p e space apostrophe m apostrophe space a n d space p a s sin g space t h r o u g h space t h e
p o i n t space open parentheses x subscript 1 comma y subscript 1 close parentheses space i s space y minus y subscript 1 equals m open parentheses x minus x subscript 1 close parentheses
T h e r e f o r e comma space t h e space r e q u i r e d space e q u a t i o n space i s
y minus 0 equals tan 45 degree open parentheses x minus 2 close parentheses
rightwards double arrow y equals 1 cross times open parentheses x minus 2 close parentheses
rightwards double arrow y equals x minus 2
rightwards double arrow x minus y minus 2 equals 0

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.5

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 1(vi)

Solution 2(i)

Solution 2(ii)

Solution 3

Solution 4

T h e space r e c tan g l e space A B C D space w i l l space h a v e space d i a g o n a l s space A C space a n d space B D
A C space p a s s e s space t h r o u g h space A open parentheses a comma b close parentheses space a n d space C open parentheses a apostrophe comma b apostrophe close parentheses. space
T h u s space e q u a t i o n space o f space A C space i s :
fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
rightwards double arrow fraction numerator y minus b over denominator b apostrophe minus b end fraction equals fraction numerator x minus a over denominator a apostrophe minus a end fraction
rightwards double arrow open parentheses y minus b close parentheses open parentheses a apostrophe minus a close parentheses equals open parentheses x minus a close parentheses open parentheses b apostrophe minus b close parentheses
rightwards double arrow y open parentheses a apostrophe minus a close parentheses minus a apostrophe b plus a b equals x open parentheses b apostrophe minus b close parentheses minus a b apostrophe plus a b
rightwards double arrow y open parentheses a apostrophe minus a close parentheses equals x open parentheses b apostrophe minus b close parentheses minus a b apostrophe plus a apostrophe b
rightwards double arrow y open parentheses a apostrophe minus a close parentheses minus x open parentheses b apostrophe minus b close parentheses equals a apostrophe b minus a b apostrophe

B D space p a s s e s space t h r o u g h space B open parentheses a apostrophe comma b close parentheses space a n d space D open parentheses a comma b apostrophe close parentheses. space
T h u s space e q u a t i o n space o f space B D space i s :
fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
rightwards double arrow fraction numerator y minus b over denominator b apostrophe minus b end fraction equals fraction numerator x minus a apostrophe over denominator a minus a apostrophe end fraction
rightwards double arrow open parentheses y minus b close parentheses open parentheses a minus a apostrophe close parentheses equals open parentheses x minus a apostrophe close parentheses open parentheses b apostrophe minus b close parentheses
rightwards double arrow minus y open parentheses a apostrophe minus a close parentheses minus a b plus a apostrophe b equals x open parentheses b apostrophe minus b close parentheses minus a apostrophe b apostrophe plus a apostrophe b
rightwards double arrow a apostrophe b apostrophe minus a b equals x open parentheses b apostrophe minus b close parentheses plus y open parentheses a apostrophe minus a close parentheses
rightwards double arrow x open parentheses b apostrophe minus b close parentheses plus y open parentheses a apostrophe minus a close parentheses equals a apostrophe b apostrophe minus a b

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

L equals 4 over 1875 C plus 124.942 minus 4 cross times 20 over 1875
rightwards double arrow L equals 4 over 1875 C plus 124.899

Solution 12

Solution 13

rightwards double arrow y minus 3 equals 1 third open parentheses x minus 4 close parentheses
rightwards double arrow 3 open parentheses y minus 3 close parentheses equals x minus 4
rightwards double arrow x minus 3 y plus 9 minus 4 equals 0
rightwards double arrow x minus 3 y plus 5 equals 0

Solution 14

Solution 15

  

 

 

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.6

Solution 1

Solution 2

Solution 3

3

Solution 4


 

 

 

Solution 5

Solution 6

 

 

Solution 7

Solution 8

Solution 9

P o i n t space left parenthesis h comma k right parenthesis space d i v i d e s space t h e space l i n e space s e g m e n t space i n space t h e space r a t i o space 1 : 2
T h u s comma space u sin g space s e c t i o n space p o i n t space f o r m u l a comma space w e space h a v e
h equals fraction numerator 2 cross times a plus 1 cross times 0 over denominator 1 plus 2 end fraction
a n d
k equals fraction numerator 2 cross times 0 plus 1 cross times b over denominator 1 plus 2 end fraction
T h e r e f o r e comma space w e space h a v e comma
h equals fraction numerator 2 a over denominator 3 end fraction space a n d space k equals b over 3
rightwards double arrow a equals fraction numerator 3 h over denominator 2 end fraction a n d space b equals 3 k
T h u s comma space t h e space c o r r e s p o n d i n g space p o i n t s space o f space A space a n d space B space a r e space open parentheses fraction numerator 3 h over denominator 2 end fraction comma 0 close parentheses space a n d space open parentheses 0 comma 3 k close parentheses
T h u s comma space t h e space e q u a t i o n space o f space t h e space l i n e space j o i n i n g space t h e space p o i n t s space A space a n d space B space i s
fraction numerator y minus 3 k over denominator 3 k minus 0 end fraction equals fraction numerator x minus 0 over denominator 0 minus fraction numerator 3 h over denominator 2 end fraction end fraction
rightwards double arrow minus fraction numerator 3 h over denominator 2 end fraction open parentheses y minus 3 k close parentheses equals x cross times 3 k
rightwards double arrow minus 3 h y plus 9 h k equals 6 k x
rightwards double arrow 2 k x plus h y equals 3 k h

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.7

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 2


 

 

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.8

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.9

Solution 1

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 2(v)

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.10

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 2(i)

Solution 2(ii)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 4

Solution 5

Solution 6(i)

Solution 6(ii)

Solution 6(iii)

Solution 7

Solution 8

Solution 9

 

Solution 10

Solution 11

 

Solution 12

Solution 13

Solution 14

 

Solution 15

Solution 16


 

 

Solution 17

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.11

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.12

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

 

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26


Solution 27


 

 

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.13

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10


 

 

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.14

Solution 1

Solution 2

Solution 3

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.15

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.16

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.17

Solution 1

Solution 2

Solution 3

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.18

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Consider the following figure:

T h e space e q u a t i o n space o f space A B space i s
y minus 2 equals 1 fifth open parentheses x minus 1 close parentheses
rightwards double arrow 5 y minus 10 equals x minus 1
rightwards double arrow x minus 5 y plus 9 equals 0
A n d space t h e space e q u a t i o n space o f space B C space i s
y minus 8 equals minus 5 open parentheses x minus 5 close parentheses
rightwards double arrow y minus 8 equals minus 5 x plus 25
rightwards double arrow 5 x plus y minus 33 equals 0

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23.19

Solution 1

Solution 2

Solution 3

rightwards double arrow fraction numerator 6 x minus 21 y plus 33 plus 7 x plus 21 y minus 56 over denominator 3 end fraction equals 0
rightwards double arrow 6 x minus 21 y plus 33 plus 7 x plus 21 y minus 56 equals 0
rightwards double arrow 13 x minus 23 equals 0
rightwards double arrow 13 x equals 23

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11


 

 

RD Sharma Solution for Class 11 Science Mathematics Chapter 23 - The Straight Lines Page/Excercise 23VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14


Solution 15

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 11. Access the CBSE Class 11 Mathematics Chapter 23 - The Straight Lines for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 23 - The Straight Lines.

Text Book Solutions

CBSE XI Science - Mathematics

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