Straight Lines NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.1 10.2 10.3 Miscellaneous Free pdf Notes Study Material download-Anand Classes
NCERT Solutions for Class 11 maths Chapter 10 Straight Lines explains analytical geometry, which is the name given to the resulting combination of analysis and geometry. From the knowledge of previous classes, the students must be aware of two-dimensional coordinate geometry, which is a mix of algebra and geometry. Students must be familiar with the basics of coordinate geometry like co-ordinate axes and planes, plotting points in a plane, how to find the distance between two points, section formulae, etc., in order to understand the NCERT solutions Class 11 maths Chapter 10 better. This lesson starts with a quick recap of the aforementioned topics before moving on to introduce students to newer concepts based on straight lines.
Download the pdf of NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines
Download NCERT Book of Class 11 Maths Chapter 10 – Straight Lines
Number of questions in each exercise of NCERT Solutions for Class 11 Maths Chapter 10 PDF- Straight Lines
This chapter extends its study to the analysis of the most simple geometric figure, that is, a straight line with the help of coordinate geometry. Students will get to explore several properties of a straight line with the help of various logical derivations and plotting graphs of the same. This entire chapter sees the use of several different formulas as well as concepts that are applied to different scenarios. Thus, it is very important for students to study with utmost focus and due diligence. Additionally, this topic is vital from an examination of point of view. The pdf file of the Class 11 maths NCERT solutions Chapter 10 Straight Lines can be found below for quick access and also download the exercise-wise solutions provided in the links below.
- NCERT Solutions Class 11 Maths Chapter 10 Ex 10.1
- NCERT Solutions Class 11 Maths Chapter 10 Ex 10.2
- NCERT Solutions Class 11 Maths Chapter 10 Ex 10.3
- NCERT Solutions Class 11 Maths Chapter 10 Miscellaneous Ex
As simple as it may look, the line is an important geometric notion that appears in our daily lives in a variety of interesting and helpful ways. A straight line has many industrial applications such as in performing linear regressions when mathematical models are created. Also, this topic makes its way into the class 12th syllabus.
The given chapter lays emphasis on algebraically representing a line, with the slope being the most important factor. students will get to learn the important facts about slope, like, the slopes of two parallel lines are equal, while if they are perpendicular, the product of their slopes is equal to -1. This chapter requires regular revision to perfect it. Children can find an exercise-wise detailed analysis of NCERT Solutions Class 11 Maths Chapter 10 Straight Lines below :
- Class 11 Maths Chapter 10 Ex 10.1 – 14 Questions
- Class 11 Maths Chapter 10 Ex 10.2 – 20 Questions
- Class 11 Maths Chapter 10 Ex 10.3 – 18 Questions
- Class 11 Maths Chapter 10 Miscellaneous Ex 10.3 – 24 Questions
Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines
Topics Covered: The Class 11 maths NCERT solutions Chapter 10 covers topics like the formula for finding the distance between two points, the distance of a point from a line, equation of a line, how to identify parallel and perpendicular lines, finding the intersection point of straight lines and the angle of inclination of the line. Further, how to get co-ordinate geometry input of a point and feed it into algebraic equations in the context of geometrical shapes to be able to measure, trace and uncover the properties of different shapes also fall under the scope of this lesson.
Total Questions: Class 11 maths Chapter 10 Straight Lines Chapter 10 consists of 76 questions of which 31 are easy, 11 are moderate, and 10 are long answer type questions. Apart from this, there are 24 miscellaneous exercise questions at the end of the chapter, which are complicated ad require higher-order thinking.
Some of the concepts discussed in Chapter 10 of NCERT Solutions for Class 11 Maths are given below.
- Slope (m) of a non-vertical line.
- If a line makes an angle á with the positive direction of the x-axis, then the slope of the line is given by m = tan α, α ≠ 90°.
- The slope of a horizontal line is zero, and the slope of a vertical line is undefined.
- Two lines are parallel if and only if their slopes are equal.
- Two lines are perpendicular if and only if the product of their slopes is –1.
- Three points A, B and C are collinear if and only if the slope of AB = slope of BC.
- The equation of the horizontal line having distance a from the x-axis is either y = a or y = – a
- The equation of the vertical line having distance b from the y-axis is either x = b or x = – b
- The point (x, y) lies on the line with slope m and through the fixed point (xo , yo ) if and only if its coordinates satisfy the equation y – yo = m (x – xo).
- The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
- If a line with slope m makes x-intercept d. Then, the equation of the line is y = m (x – d).
- The equation of the line having a normal distance from the origin p and angle between normal and the positive x-axis ω is given by cosω+ sinω = pyx.
- Any equation of the form Ax + By + C = 0, with A and B, not zero, simultaneously, is called the general linear equation or general equation of a line
Brief recall of two-dimensional geometry from earlier classes, Shifting of origin, Slope of a line and angle between two lines, Various forms of equations of a line: parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form, General equation of a line, equation of the family of lines passing through the point of intersection of two lines, the distance of a point from a line are the topics that the students must have grasped by learning these concepts.
List of Formulas in NCERT Solutions Class 11 Maths Chapter 10 – Straight Lines
NCERT solutions Class 11 maths Chapter 10 is a recognition of reaching a point in mathematics wherein we are now capable of using different branches of mathematics and see the beauty of how one translates into the other or how input from one branch of mathematics feeds into another stream of mathematics to unearth more information or patterns. Starting with the very building block, that is, a single point that can be mapped using the distance it has from two perpendicular axes. This lays the groundwork for an altogether new dimension where we are introduced to the next logical shape after a point that is of a line that can be defined by any two points on it. Equation of a line, its simplicity, and its completeness in defining the trajectory of a point is an important takeaway.
Some important formulas covered in NCERT Solutions for Class 11 maths Chapter 10 are given below:
- Slope of line passing through the points (x1, y1) and (x2,y2) : m = ( y2 – y1 ) /( x2 – x1 )
- Any point (x, y) with slope ‘m’ and y-intercept ‘c’ lies on the line if only y = mx + c.
- Any line with slope ‘m’ that has x-intercept as ‘d’, in that case, its equation is y = m (x – d)
- Equation of a line when it makes intercepts ‘a’ and ‘b’ on the x-and y-axis : x/a + y/b = 1
Frequently Asked Questions (FAQs) on NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines
Why are NCERT Solutions Class 11 Maths Chapter 10 Important?
The NCERT solutions class 11 maths chapter 10 has elaborated on the concept of coordinate geometry to understand the geometrical shapes. This forms an important concept in the field of mathematics as several concepts of algebra and trigonometry are entwined here. The experts at NCERT have come up with good explanatory examples and exercise questions making it easier for the students to understand this topic. The CBSE board also asks the students to refer to the NCERT books for their exams, making them of utmost importance.
Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Straight Lines?
The more the students will practice the sums, the better they will get at exploring the different viewpoints and case studies of problems. This will enhance their confidence in problem-solving as well as memorizing the concepts. students should also practice the solved examples given in the NCERT Solutions Class 11 Maths Straight Lines by themselves. Thus, it is advantageous on many levels for young minds to practice all the questions.
What are the Important Topics Covered in Class 11 Maths NCERT Solutions Chapter 10?
The NCERT Solutions Class 11 Maths Chapter 10 covers analytical geometry with the help of coordinate geometry. It has topics like the formula for the equation of a line, for finding the distance between two points, and distance of a point from a line, as well as identifying parallel and perpendicular lines. How to work with algebraic equations in the context of geometrical shapes, as well as the logic behind uncovering the properties of different shapes, is explained with well-illustrated examples.
How Many Questions are there in NCERT Solutions Class 11 Maths Chapter 10 Straight Lines?
The NCERT Solutions Class 11 Maths Chapter 10 Straight Lines has 52 questions; 31 of them are easy, 11 are moderate, and 10 may need some extra time. Also, there are 24 miscellaneous exercise questions at the end of the chapter. These are necessary to solve as they will give extra knowledge on the concepts learned. These questions span all the sections covered under this chapter in a more practical way.
How CBSE Students can utilize NCERT Solutions Class 11 Maths Chapter 10 effectively?
The NCERT Solutions Class 11 Maths Chapter 10 has well-curated content prepared by eminent scholars in an easy language which is used in solved examples as well. The students must attempt all examples and exercise questions. Also, important formulas and facts are presented in the highlights section of the chapter at the end, which the students should take note of. In this way, these solutions can be utilized in the most effective way.
Why Should I Practice NCERT Solutions Class 11 Maths Straight Lines Chapter 10?
To gain an extra edge on problem-solving and mental math skills, the students must refer to NCERT Solutions Class 11 Maths Straight Lines Chapter 10. These solutions will provide sufficient practice on the coordinate geometry concepts and the analysis of the same. These topics are required for higher classes as well, so it is essential to polish them as early as possible.
Mention the topics and subtopics covered in Chapter 10 of NCERT Solutions for Class 11 Maths.
10.2 Slope of a Line
10.2.1 Slope of a line when coordinates of any two points on the line are given
10.2.2 Conditions for parallelism and perpendicularity of lines in terms of their slopes
10.2.3 Angle between two lines
10.2.4 Collinearity of three points
10.3 Various Forms of the Equation of a Line
10.3.1 Horizontal and vertical lines
10.3.2 Point-slope form
10.3.3 Two-point form
10.3.4 Slope-intercept form
10.3.5 Intercept – form
10.3.6 Normal form
10.4 General Equation of a Line
10.4.1 Different forms of Ax + By + C = 0
10.5 Distance of a Point From a Line
10.5.1 Distance between two parallel lines
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