NCERT Solutions Class 11 Maths Chapter 10

NCERT Solutions for Class 11 Mathematics Chapter 10 – Straight lines

Mathematics helps build the students’ analytical mindset. The various numerical and activities covered in the NCERT Solutions help students think more smartly. Due to this, students start thinking logically and develop a right perspective while solving mathematical problems. 

Class 11 Mathematics Chapter 10 introduces the Coordinate Geometry section of NCERT Class 11 Mathematics. The Coordinate unit of Geometry includes chapters like Straight lines, Circles, Parabola and Hyperbola covered in Class 11 and 12 Mathematics. It plays an essential role in various competitive examinations and is a highly scoring unit. Hence, students must try to make the concepts of the Straight chapter lines strong to be good at it. . Straight lines cover the basics of Circle, Parabola and Hyperbola. As a result, it becomes a crucial chapter in Class 11 Mathematics.

NCERT Solutions for Class 11 Mathematics Chapter 10 will help you build a solid conceptual understanding of the chapter Straight  Lines. It will also aid you in connecting to the concepts of the chapters of Coordinate Geometry.  It has multiple questions on the topics covered in the chapter, giving students confidence while performing calculations. It will also bridge the gap between basic and advanced Mathematics. Thus, making students confident enough to face competitive examinations.

Extramarks has built its credibility due to constant appreciation from parents,  teachers and students alike. Extramarks experienced faculty prepares authentic, concise answers which students can trust and enjoy the process of learning. As a result, it is known as one of the fastest-growing online platforms for all NCERT-related study material. Students can find NCERT textbooks, NCERT solutions, NCERT revision notes, NCERT-based papers and all the mock tests designed per the NCERT curriculum available on the Extramarks’ website.

Key Topics Covered in Class 11 Mathematics Chapter 10

Students would already know that when two points are placed randomly and joined together, it forms a straight line. Straight lines are used almost everywhere, whether you draw a graph or a map, a parabola or a hyperbola, a rectangle, or a square. Therefore, it lays the foundation for basic geometry. 

All the basics covered in the Straight Lines will be strongly used in other chapters of Coordinate Geometry like circle, hyperbola and parabola. The main topics covered in this chapter include the slope of a line, the angle between two lines, the condition for parallelism and perpendicularity, the collinearity of three points and the various equations. Students can access the NCERT solutions from the Extramarks’ website.

NCERT Solutions for Class 11 Mathematics Chapter 10 require students to enhance their understanding through real life examples with activities during their learning process.

Introduction

In earlier classes,  students have learned about topics like two dimensions and coordinate geometry. The topics like coordinate axes, coordinate plane, plotting points in the plane, the distance between two points, and the section formula were covered in coordinate geometry.

There is some formula which is related to straight lines, which are given below:

• The distance between the point P (x1 ,y1)and Q (x2 ,y2) is 

PQ = √[(x2-x1)2 + (,y2-y1)2]

• The coordinate of a point dividing the line segment joining the point (x1 ,y1) and (x2 ,y2) internally in the ratio m : n is

[(m.x2 + n. x1)/(m + n) , (m.y2 + n. y1)/(m + n)]

• In particular, if m = n, the coordinate of the midpoint of the line segment joining the points (x1 ,y1) and (x2 ,y2) are

[(x1+x2)/2 , (y1+y2)/2

• Area of the triangle whose vertex is

(1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] 

Remark: if we have a triangle ABC whose area is equal to zero, then the point ABC lies on a line. This is called collinear. 

As in the earlier chapter, we studied a straight line. In this chapter, we will cover all the concepts related to straight lines. 

The complete chapter straight lines is covered in detail in the NCERT Solutions for Class 11 Mathematics Chapter 10.

The slope of a line  

• The inclination of the line: When the line is making an angle θ with the positive side of the x-axis and measures anti-clockwise, it’s called the inclination of the line.

Definition

If there is a line with the length of L and that is making inclination with the line, then Tan θ is called the slope or gradient of the line.

m = Tan θ 

• Slope of a line when coordinates of any two points on the line are given.

The different cases are listed below:

• Case 1: when the angle is acute 
• Case 2: when the angle is obtuse. 

In both the cases for slope m of the line through the point (x1 ,y1) and (x2 ,y2) are given by,

m = (y2-y1)/(x2-x1)

The entire concept related to the slope of a line and all the associated concepts interconnected with it in the NCERT Solutions for Class 11 Mathematics Chapter 10 available on the Extramarks’ website.

• Conditions for parallelism and perpendicularity of lines in terms of their slopes

• • If two lines, L1 and L2, are parallel, then their slopes will be:

m1 = m2

• If two lines, L1 and L2, are perpendicular, then their slope will be:

m1.m2= -1

• Angle between two lines

In this section, we will calculate the angle between two lines as follows:

• Case 1

If (m2– m1) / (1+ m1.m2) is positive, then Tan θ will be positive, and when Tan Ø is negative, which means θ will be acute and Ø will be obtuse.

• Case 2

If (m2– m1) / (1+ m1.m2) is Negative, then Tan θ will be negative, and then tan Ø will be positive, which means θ will be obtuse and Ø will be acute.

Tan θ = | (m2– m1) / (1+ m1.m2)|, as 1+ m1.m2 ≠ 0

All the cases of angle between two lines are further explained in our NCERT Solutions for Class 11 Mathematics Chapter 10. Students can register on Extramarks’ website and access  NCERT solutions.

• Collinearity of three points. 

In this chapter, we will learn that if two lines with the same slope pass through a common point, two lines will coincide.

First-line slope  = second-line slope

Various Forms of the Equation of a Line 

• Horizontal and vertical lines
• Equation of a horizontal line

 Y = a, Y =-a

• Equation of a vertical line 

X = b, X = -b

• Point–slope form

In this section, we will calculate the distance from a fixed point to the other point with the slope of m, which is given below:

m =  (y – y0) / (x-x0) 

• Two-point form

The line passing through two given points (x1 ,y1) and (x2 ,y2) from a general point (x,y) is called the two-point form of a line. The formula of the two-point form of a line is given by 

 (y – y1) / (x-x1) = (y2-y1) / (x2-x1)

• Slope intercept form.

We will find the equation of a line when the slope and intercept are given using the slope-intercept form. The formula used for calculating using the slope-intercept form is 

y = m.x + c

• Intercept- form.

The formula for the intercept form is derived from the two points. From the equation of the line, it is given as

X/a+ Y/b=1

• Normal form.

If a non-vertical line is known to us, then the length of the perpendicular or normal from the origin to the line and the angle that the normal makes with the positive direction of the x-axis can be calculated.

X.cosω + y.sinω = p

The various forms related to the equation of a line are covered in detail in the NCERT Solutions for Class 11 Mathematics Chapter 10.

• Alternate method

For calculating the slope of the line on the line equation apart from the above-studied methods, we can use some alternative methods assuming constant and get quick answers.

K = mF + c

You can find step by step solutions to alternative methods in the NCERT Solutions for Class 11 Mathematics Chapter 10.

General Equation of a Line 

There are three types of writing a general equation of a line. The different forms of Ax + By + C = 0 are

• Slope intercept form

Slope = -A/B, Y-intercepts = -C/B, X-intercept= -C/A

• Intercept form

Y-intercepts = -C/B, X-intercept= -C/A

• Normal form

             Cosω = ±A/√(A2+B2)

                            Sinω =   ±B/√(A2+B2)

                            P = ±C/√(A2+B2)

Distance of a Point From a Line

In this section of the chapter, we will calculate the perpendicular distance of a line from a point, and its formula is given:

• Distance between two parallel lines

The distance between two parallel lines is given by

• For the line equation; y = mx+c1, y = mx+c2

d = |C1+C2|/√1 + m2

• For the line equation; Ax + By + C1 = 0, Ax + By + C2 = 0

d = |C1+C2|/√(A2+B2)

You can find a lot of questions to practice on this topic in the NCERT Solutions for Class 11 Mathematics Chapter 10 available on the Extramarks’ website.

NCERT Solutions for Class 11 Mathematics Chapter 10 Exercise &  Solutions.

Extramarks NCERT Solutions for Class 11 Mathematics Chapter 10 has a detailed solution of all the exercises covered in the NCERT textbook. Students can access it by registering on the website. They can also find a lot of additional questions to practise that will definitely prove useful while solving advanced-level problems. It helps them to know how to solve the different kinds of problems in  a step-by-step manner.  They learn to use simple tricks to solve it quickly, ensuring that students complete their paper on time.

Click on the  links below to view exercise-specific questions and solutions available in our NCERT Solutions for Class 11 Mathematics Chapter 10:

• Class 11 Mathematics Chapter 10: Exercise 10.1 
• Class 11 Mathematics Chapter 10: Exercise 10.2
• Class 11 Mathematics Chapter 10: Exercise 10.3. 
• Class 11 Mathematics Chapter 10: Miscellaneous Exercises

Along with Class 11 Mathematics solutions, you can explore NCERT Solutions on our Extramarks’ website for all primary and secondary classes 

• NCERT Solutions Class 1
• NCERT Solutions Class 2
• NCERT Solutions Class 3
• NCERT Solutions Class 4
• NCERT Solutions Class 5
• NCERT Solutions Class 6
• NCERT Solutions Class 7
• NCERT Solutions Class 8
• NCERT Solutions Class 9
• NCERT Solutions Class 10
• NCERT Solutions Class 11
• NCERT Solutions Class 12

NCERT Exemplar Class 11 Mathematics

NCERT Exemplar Class 11 Mathematics has always been a perfect choice for students requiring extra guidance and for teachers who need more questions for the students to get extra practice.  Since the book covers the sets of questions from the core topics in the chapter,    no wonder it has become the most sought after and trusted book in the market by the students preparing for competitive examinations like JEE, NEET, MHT-CET, BITSAT, VITEEE etc.

After a complete overview of the chapters of the NCERT textbook, the subject matter experts have designed and written the NCERT Exemplar. All the solutions are provided by experienced faculty of Extramarks.. Students can find concepts covered in the form of questions that not only pushes them to practice more but also helps them rectify their mistakes wherever required.

The answers will help students clearly understand how they need to approach a particular question. This will definitely improve  their scores and thereby help to boost their confidence during the exam preparation. Students can get NCERT Exemplar Class 11 Mathematics from the Extramarks’ website and leverage their performance in the examinations.

Key Features for NCERT Solutions for Class 11 Mathematics Chapter 10

Extramarks is one of the most popular online learning study platforms for lakhs of students preparing for Class 11 and Class 12. We understand that students require a lot of handholding and guidance to stay focused and prepare well for their examinations.

Students require certain skill sets to study well and to solve their exam papers properly. Hence, NCERT Solutions for Class 11 Mathematics Chapter 10 also focuses on building the right skills among students to accelerate in their preparedness for the exams. . 

The key features of our NCERT Solutions are as below: 

•  Extramarks academic experts from various disciplines have prepared the study materials after researching and analysing NCERT textbooks, Exemplar books, reference study materials and past years’ question papers
• After completing the NCERT Solutions for Class 11 Mathematics Chapter 10, students will be able to think, learn and solve problems  in a better way.
• Students will learn the art of time management, increase your focus and enhance your productivity once they refer to NCERT Solutions for Class 11 Mathematics Chapter 10.
• They will  be able to grasp the concepts and turn into smart learners and solve problems without much difficulty after going through these solutions.