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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.
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