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

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 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 :
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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
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