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RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.4) Exercise 23.4

Last updated date: 09th Aug 2024
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RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.4) Exercise 23.4 - Free PDF

Free PDF download of RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines Exercise 23.4 solved by Expert Mathematics Teachers on Vedantu. All Concepts of the Chapter 23 - The Straight Lines Ex 23.4 Questions with Solutions for RD Sharma Class 11 Math help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

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RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines

The focus of RD Sharma Class 11 chapter 23 is on lines and straight lines. It is explained in a simplified way to ensure students understand it all with ease. We have covered these topics here and ensured the explanations are detailed and simple for students to grasp. With the help of the solutions provided by Vedantu, students will be fully equipped to handle all questions from this chapter.

In this exercise, we will be looking at the following topics:

The slope of a line, Horizontal and vertical lines, Point-slope form, Two-point form, Slope-intercept form, Intercept-form, and Normal form.

Let us give you a brief introduction to a few.

What is the slope of a line?

A line is said to be sloped if its slope, the ratio of the change in y to the change in x when x and y are varied separately, is nonzero. The slope of a line may be written as either a fraction, a decimal, or a fractional equivalent.

In the first case, the fraction is the change in y divided by the change in x. The expression a/b means that a = number of changes in y, and b = change in x. If the change in y is negative, then a is negative, and the negative is converted to a fraction by multiplying by -1.

The slope of a line may be defined as the ratio of the change in y to the change in x when x and y are varied separately.

To determine whether a line of slope m passes through the origin of the coordinate system is horizontal, vertical, or neither, we need to know the value of m. This is because the x and y-intercepts are expressed as functions of m, and a line is horizontal when its x-axis intercept is zero and its y-axis intercept is not, and a line is vertical when its x-axis intercept is not zero and its y-axis intercept is zero, and it is neither horizontal nor vertical when its x-axis intercept is not zero and its y-axis intercept is zero.

Here is an Example from the exercise :

Find the equation of the straight line which passes through the point (1, 2) and makes such an angle with the positive direction of the x – axis whose sine is $\frac{3}{5}$.

Solution:

A line which is passing through (1, 2)

To Find: The equation of a straight line.

By using the formula,

The equation of line is [y – y1 = m(x – x1)]

Here, sin θ = $\frac{3}{5}$

We know, sin θ = perpendicular/hypotenuse = $\frac{3}{5}$

So, according to Pythagoras theorem,

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

(5)2 = (Base)2 + (3)2

(Base) = $\sqrt{(25-9)}$

(Base)2 = $\sqrt{16}$

Base = 4

Hence, tan θ = $\frac{Perpendicular}{Base}$

= $\frac{3}{4}$

The slope of the line, m = tan θ

= $\frac{3}{4}$

The line passing through (x1,y1) = (1,2)

The required equation of line is y – y1= m(x – x1)

Now, substitute the values, we get

y – 2 = $\frac{3}{4}$(x – 1)

4y – 8 = 3x – 3

3x – 4y + 5 = 0

∴ The equation of line is 3x – 4y + 5 = 0

We at Vedantu hope that you make the best of this book and the resources that we provide you. All the best!

FAQs on RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.4) Exercise 23.4

1. What do students learn in the chapter- The straight Lines?

Class 11 mathematics gives students an in-depth yet fundamentals of various concepts which are useful in pursuing mathematics further in their education. Chapter 23 Straight lines in class 11 are one of the important and interesting topics that elaborate on the basic concepts of lines such as slopes, the angle between two lines, various forms of lines, and much more. A straight line is the simplest shape in geometry but it covers a major part.

2. Where can I find the solutions of class 11 Chapter 23 exercise 23.4 straight lines?

Class 11 mathematics is a core subject to students who opt for mathematics in this stage. The chapter of straight lines revolves around various concepts related to straight lines starting from the very basics. Vedantu is a platform that aims at making students well prepared for the final exams and therefore it provides answers to all the questions created by expert subject teachers which can be downloaded either through the Vedantu app or website.

3. What are the suggested books for class 11 straight lines?

Straight lines in class 11 is one of the important and interesting topics that cover the basic concepts of lines such as slopes, the angle between two lines, various forms of lines, and more. For a class 11 student, a few suggested books are the NCERT textbook and RD Sharma. In addition to this, Vedantu also provides students with adequate study material and notes which makes it not only easier but also interesting for the students. Such study material helps students grasp and retain the concepts for a longer duration. To find notes, visit the Vedantu app or website.

4. What is the charge to download the solutions of class 11 Chapter 23 exercise 23.4 straight lines?

To download the class 11 mathematics chapter 23 exercise 23.4 The Straight Lines solutions PDF, students need not pay anything. We aim to provide students with solutions containing the best and easy explanations that give clarity to the students. All that students need to do is go to the Vedantu app or website, search for this chapter, and click download. Also, students are provided with the solutions in PDF format by Vedantu that helps them easily access them.