NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines
NCERT Solutions for Class 11 Maths Chapter 10 cover the very essential topic of straight lines from the CBSE exam perspective. The solutions given here can be helpful for anyone who wishes to improve their score in the CBSE Maths Examination or who wants to prepare the topic for entrance exams like JEE and NEET. We have provided all the solutions in a straightforward and detailed manner for your convenience.
NCERT Class 11 Maths Chapter 10 has a total of 52 questions covering the different concepts of the chapter and 3 exercises. The exercises have been devised to ensure that you can test your retention capacity and to anticipate the kind of questions you will be asked in the exams. For solving these exercises, NCERT solutions for Maths Chapter 10 can be your fruitful guide.
In this chapter, you are going to learn some very important topics of geometry such as straight line, equation of the straight line, intercept form, point form, slope point form, the relation between two lines, angles between the two lines and many more. Given below is a quick summary of the chapter that will help you revise the topics easily.
Important Topics for NCERT Solutions for Class 11 Maths Chapter 10
Basically, chapter 10 of NCERT Solutions for Class 11 Maths Textbook allows you to recall the concept of two-dimensional geometry and then introduces some new topics. A basic understanding of straight lines and also the advanced topics are covered in-depth so that you can be well-versed with the concepts. Here are some of the essential things that you should remember from this chapter:
Equation of Line
Equation of a line is ax+by+c=0 (x and y are variables and a, b and c are constants). Variations of the equation of a straight line depending on the different situations:
- Line parallel to X-axis: y=b
- Line parallel to Y-axis: x=a
- X-axis equation: y=0
- Y-axis equation: x=0
- When a line with slope m intercept at point c on the Y-axis, then the equation is y=mx+c and is known as slope-intercept form.
- When a line with slope m passes through points x1, y1, then equation is (y – y1) = m (x – x1) and is called one-point slope form.
- When a line passes through points x1,y1 and x2, y2, then the equation is (y – y1) = (y2 – y1 / x2 – x1) (x – x1) and is known as a two-point form.
- When a line intercepts at points a and b on X-axis and Y-axis, then the equation is x / a + y / b = 1 and is termed as intercept form.
- When the angle made by perpendicular on the line is α and perpendicular length from the origin of the line is p, then the equation is x cos α + Y sin α = p and is known as a normal form.
- Last but not the least, the distance form is x – x1 / cos θ = y – y1 / sin θ = r, when the line passes through x1,y1 and makes an angle θ with the positive direction of the x-axis.
- Along with these, the equation of line parallel or perpendicular to another given line is also discussed in this chapter.
The slope of a Line
The slope of a line is m= tan θ (θ is basically the angle the line makes with the positive direction of the X-axis). Variations of the slope of lines depending on the different situations:
- Line parallel to X-axis- m=0
- Line parallel to Y-axis- m = ∞
Slope of line passing through x1,y1 and x2, y2: m = tan θ = y2 – y1 / x2 – x1
Angles between the Two Lines
- Acute angle- tan θ=[m2-m1/1+ m1 m2], 1 m1 m2 ≠0
- Obtuse angle- Ø= 180- α
- If slope m1=slope m2, then the lines are parallel to one another.
- If the slope is m1 m2=-1, then the lines are perpendicular to each other.
Other Things Covered in the Chapter
Position of two points on a given line whether they are on the same side or opposite side and other positions with respect to the line have also been explained. Images of points with respect to the line and equation of bisectors are some other topics covered in chapter 10 of NCERT Maths Textbook. For more details on this chapter, you must go through the textbook or the revision notes itself given in the form of NCERT Solutions for Class 11 Maths Chapter 10 by the Instasolv experts.
Discussion of Exercises of NCERT Class 11 Maths Chapter 10
- Exercise 10.1 in the NCERT textbook has questions related to drawing quadrilaterals with the given vertices, finding vertices of a triangle, finding distances between two given points on the basis of certain conditions, finding the slope of lines and so on.
- Exercise 10.2 has a majority of questions associated with finding the equation of a line on the basis of certain conditions given in the questions so you can solve this for much clarity of this topic of chapter 10.
- While in the last exercise: Exercise 10.3, get ready to learn how to reduce equations into intercept form or normal form and also finding distance between a point and a given line and distance between parallel lines and so on.
Benefits of NCERT Solutions for Class 11 Maths Chapter 10 by Instasolv
All the exercise solutions of NCERT Class 11 maths chapter 10 are created in a step-wise manner by our maths experts. All the solutions adhere to the CBSE guidelines so you can easily rely on them for exam preparation. You can also refer to them while doing your homework and find quick solutions to your doubts without any hassle. Our experts check the solutions at least twice at various phases so we ensure you the best quality and complete accuracy.