All Courses
Get the App Signup / Login
Sign in Open App
Commerce Exam  >  Commerce Notes  >  Mathematics (Maths) Class 11  >  RD Sharma Class 11 Solutions Chapter - The Straight Lines

RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


23. The Straight Lines
Exercise 23.1
1 A. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan  = – 1
Hence, The slope of the line is – 1.
1 B. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is .
1 C. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Page 2


23. The Straight Lines
Exercise 23.1
1 A. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan  = – 1
Hence, The slope of the line is – 1.
1 B. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is .
1 C. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is – 1.
1 D. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan ?
So, The slope of Line is m = tan 
Hence, The slope of the line is v3.
2 A. Question
Find the slopes of a line passing through the following points :
(– 3, 2) and (1, 4)
Answer
Given (– 3, 2) and (1, 4)
To Find The slope of the line passing through the given points.
Page 3


23. The Straight Lines
Exercise 23.1
1 A. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan  = – 1
Hence, The slope of the line is – 1.
1 B. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is .
1 C. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is – 1.
1 D. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan ?
So, The slope of Line is m = tan 
Hence, The slope of the line is v3.
2 A. Question
Find the slopes of a line passing through the following points :
(– 3, 2) and (1, 4)
Answer
Given (– 3, 2) and (1, 4)
To Find The slope of the line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
2 B. Question
Find the slopes of a line passing through the following points :
(at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
Answer
Given (at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
To Find: The slope of the line passing through the given points.
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
m = 
[Since, (a
2 –
 b
2
 = (a – b)(a + b)]
m = 
Hence, The slope of the line is 
2 C. Question
Find the slopes of a line passing through the following points :
(3, – 5) and (1, 2)
Answer
Given (3, – 5) and (1, 2)
To Find: The slope of line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
3 A. Question
Page 4


23. The Straight Lines
Exercise 23.1
1 A. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan  = – 1
Hence, The slope of the line is – 1.
1 B. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is .
1 C. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is – 1.
1 D. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan ?
So, The slope of Line is m = tan 
Hence, The slope of the line is v3.
2 A. Question
Find the slopes of a line passing through the following points :
(– 3, 2) and (1, 4)
Answer
Given (– 3, 2) and (1, 4)
To Find The slope of the line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
2 B. Question
Find the slopes of a line passing through the following points :
(at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
Answer
Given (at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
To Find: The slope of the line passing through the given points.
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
m = 
[Since, (a
2 –
 b
2
 = (a – b)(a + b)]
m = 
Hence, The slope of the line is 
2 C. Question
Find the slopes of a line passing through the following points :
(3, – 5) and (1, 2)
Answer
Given (3, – 5) and (1, 2)
To Find: The slope of line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
3 A. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (5, 6) and (2, 3); through (9, – 2) and (6, – 5)
Answer
We have given Coordinates off two lines.
Given: (5, 6) and (2, 3); (9, – 2) and 96, – 5)
To Find: Check whether Given lines are perpendicular to each other or parallel to each other.
Concept Used: If the slopes of this line are equal the lines are parallel to each other. Similarly, If the product
of the slopes of this two line is – 1, then lines are perpendicular to each other.
The formula used: Slope of a line, m = 
Now, The slope of the line whose Coordinates are (5, 6) and (2, 3)
So, m
1
 = 1
Now, The slope of the line whose Coordinates are (9, – 2) and (6, – 5)
So, m
2
 = 1
Here, m
1 =
 m
2 =
 1
Hence, The lines are parallel to each other.
3 B. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (9, 5) and (– 1, 1); through (3, – 5) and 98, – 3)
Answer
We have given Coordinates off two line.
Given: (9, 5) and (– 1, 1); through (3, – 5) and (8, – 3)
To Find: Check whether Given lines are perpendicular to each other or parallel to each other.
Concept Used: If the slopes of this line are equal the the lines are parallel to each other. Similarly, If the
product of the slopes of this two line is – 1, then lines are perpendicular to each other.
The formula used: Slope of a line, m = 
Now, The slope of the line whose Coordinates are (9, 5) and (– 1, 1)
Page 5


23. The Straight Lines
Exercise 23.1
1 A. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan  = – 1
Hence, The slope of the line is – 1.
1 B. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with the positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is .
1 C. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan?
So, The slope of Line is m = tan 
Hence, The slope of the line is – 1.
1 D. Question
Find the slopes of the lines which make the following angles with the positive direction of x - axis :
Answer
Given 
To Find: Slope of the line
Angle made with positive x - axis is 
The Slope of the line is m
Formula Used: m = tan ?
So, The slope of Line is m = tan 
Hence, The slope of the line is v3.
2 A. Question
Find the slopes of a line passing through the following points :
(– 3, 2) and (1, 4)
Answer
Given (– 3, 2) and (1, 4)
To Find The slope of the line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
2 B. Question
Find the slopes of a line passing through the following points :
(at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
Answer
Given (at
2
1
, 2at
1
) and (at
2
2
, 2at
2
)
To Find: The slope of the line passing through the given points.
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
m = 
[Since, (a
2 –
 b
2
 = (a – b)(a + b)]
m = 
Hence, The slope of the line is 
2 C. Question
Find the slopes of a line passing through the following points :
(3, – 5) and (1, 2)
Answer
Given (3, – 5) and (1, 2)
To Find: The slope of line passing through the given points.
Here,
The formula used: Slope of line = 
So, The slope of the line, m = 
m = 
Hence, The slope of the line is 
3 A. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (5, 6) and (2, 3); through (9, – 2) and (6, – 5)
Answer
We have given Coordinates off two lines.
Given: (5, 6) and (2, 3); (9, – 2) and 96, – 5)
To Find: Check whether Given lines are perpendicular to each other or parallel to each other.
Concept Used: If the slopes of this line are equal the lines are parallel to each other. Similarly, If the product
of the slopes of this two line is – 1, then lines are perpendicular to each other.
The formula used: Slope of a line, m = 
Now, The slope of the line whose Coordinates are (5, 6) and (2, 3)
So, m
1
 = 1
Now, The slope of the line whose Coordinates are (9, – 2) and (6, – 5)
So, m
2
 = 1
Here, m
1 =
 m
2 =
 1
Hence, The lines are parallel to each other.
3 B. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (9, 5) and (– 1, 1); through (3, – 5) and 98, – 3)
Answer
We have given Coordinates off two line.
Given: (9, 5) and (– 1, 1); through (3, – 5) and (8, – 3)
To Find: Check whether Given lines are perpendicular to each other or parallel to each other.
Concept Used: If the slopes of this line are equal the the lines are parallel to each other. Similarly, If the
product of the slopes of this two line is – 1, then lines are perpendicular to each other.
The formula used: Slope of a line, m = 
Now, The slope of the line whose Coordinates are (9, 5) and (– 1, 1)
So, m
1
 = 
Now, The slope of the line whose Coordinates are (3, – 5) and (8, – 3)
So, m
2
 = 
Here, m
1
 = m
2
 = 
Hence, The lines are parallel to each other.
3 C. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Through (6, 3) and (1,1); through (– 2, 5) and (2, – 5)
Answer
We have given Coordinates off two line.
Given: (6, 3) and (1,1) and (– 2, 5) and (2, – 5)
To Find: Check whether Given lines are perpendicular to each other or parallel to each other.
Concept Used: If the slopes of this line are equal the the lines are parallel to each other. Similarly, If the
product of the slopes of this two line is – 1, then lines are perpendicular to each other.
The formula used: Slope of a line, m = 
Now, The slope of the line whose Coordinates are (6, 3) and (1, 1)
So, m
1
 = 
Now, The slope of the line whose Coordinates are (– 2, 5) and (2, – 5)
So, m
2
 = 
Here, m
1
m
2 =
 
m
1
m
2 =
 – 1
Hence, The line is perpendicular to other.
3 D. Question
State whether the two lines in each of the following are parallel, perpendicular or neither :
Read More
75 videos|238 docs|91 tests
Join Course for Free

Top Courses for Commerce

Related Exams
About this Document
4.86/5 Rating
Dec 31, 2024 Last updated
Document Description: RD Sharma Class 11 Solutions Chapter - The Straight Lines for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Class 11 Solutions Chapter - The Straight Lines have been prepared according to the Commerce exam syllabus. Information about RD Sharma Class 11 Solutions Chapter - The Straight Lines covers topics like and RD Sharma Class 11 Solutions Chapter - The Straight Lines Example, for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 11 Solutions Chapter - The Straight Lines.
Introduction of RD Sharma Class 11 Solutions Chapter - The Straight Lines in English is available as part of our Mathematics (Maths) Class 11 for Commerce & RD Sharma Class 11 Solutions Chapter - The Straight Lines in Hindi for Mathematics (Maths) Class 11 course. Download more important topics related with notes, lectures and mock test series for Commerce Exam by signing up for free. Commerce: RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce
Description
Full syllabus notes, lecture & questions for RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce - Commerce | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 11 | Best notes, free PDF download
Information about RD Sharma Class 11 Solutions Chapter - The Straight Lines
In this doc you can find the meaning of RD Sharma Class 11 Solutions Chapter - The Straight Lines defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 11 Solutions Chapter - The Straight Lines theory, EduRev gives you an ample number of questions to practice RD Sharma Class 11 Solutions Chapter - The Straight Lines tests, examples and also practice Commerce tests
75 videos|238 docs|91 tests
Join Course for Free
Download as PDF
Explore Courses for Commerce exam

Top Courses for Commerce

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

ppt

,

practice quizzes

,

past year papers

,

mock tests for examination

,

pdf

,

Previous Year Questions with Solutions

,

Summary

,

RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce

,

MCQs

,

Objective type Questions

,

Exam

,

shortcuts and tricks

,

RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce

,

Free

,

Sample Paper

,

Semester Notes

,

study material

,

video lectures

,

Important questions

,

Viva Questions

,

Extra Questions

,

RD Sharma Class 11 Solutions Chapter - The Straight Lines | Mathematics (Maths) Class 11 - Commerce

;
Additional Information about RD Sharma Class 11 Solutions Chapter - The Straight Lines for Commerce Preparation

RD Sharma Class 11 Solutions Chapter - The Straight Lines Free PDF Download

The RD Sharma Class 11 Solutions Chapter - The Straight Lines is an invaluable resource that delves deep into the core of the Commerce exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 11 Solutions Chapter - The Straight Lines now and kickstart your journey towards success in the Commerce exam.

Importance of RD Sharma Class 11 Solutions Chapter - The Straight Lines

The importance of RD Sharma Class 11 Solutions Chapter - The Straight Lines cannot be overstated, especially for Commerce aspirants. This document holds the key to success in the Commerce exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Class 11 Solutions Chapter - The Straight Lines Notes

RD Sharma Class 11 Solutions Chapter - The Straight Lines Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Class 11 Solutions Chapter - The Straight Lines. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 11 Solutions Chapter - The Straight Lines Notes on EduRev are your ultimate resource for success.

RD Sharma Class 11 Solutions Chapter - The Straight Lines Commerce Questions

The "RD Sharma Class 11 Solutions Chapter - The Straight Lines Commerce Questions" guide is a valuable resource for all aspiring students preparing for the Commerce exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Class 11 Solutions Chapter - The Straight Lines on the App

Students of Commerce can study RD Sharma Class 11 Solutions Chapter - The Straight Lines alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Class 11 Solutions Chapter - The Straight Lines, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Class 11 Solutions Chapter - The Straight Lines is prepared as per the latest Commerce syllabus.
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup