NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.1

Class 10 is undoubtedly one of the most important years during the education of a student. It is the year when students have to appear for the board examinations that hold remarkable significance in the career of a student. Students in Class 10 experience  challenges that they have not faced before, as the board examinations are a new experience for them. The lessons that students are taught in Class 10 influence them throughout their life. The knowledge gained in Class 10 is applied in a variety of ways throughout a person’s lives.. Each topic learnt in Class 10 can play a significant role for students in students’ success.. It requires tremendous effort for students in Class 10 to achieve success in Class 10 board examinations. Being successful in the Class 10 board examinations can help students throughout their careers. The results of the Class 10 board examinations are an important factor for admissions into various institutes of higher education. Being a significant indicator of a student’s academic performance, the results of Class 10 are also taken into consideration for admissions to colleges and universities as well as for securing employment opportunities in the future. Performing well in the board examinations for Class 10 will also boost the confidence of the students and will make them not fear other examinations in the future. They can consequently perform better in any examination in the future. Students are required to study a variety of subjects in Class 10. As a result, Class 10 serves as an important year for students to make important career decisions. Following the completion of Class 10, students are required to make decisions about choosing a stream based on their interests and abilities. They can identify their subjects of interest and choose a suitable career for themselves subsequently.

For students of Class 10, Mathematics is one of the most significant and challenging subjects. Mathematics requires a tremendous amount of practisein problem-solving in addition to a deep comprehension of the principles. It is necessary to practise a lot of questions if one wants to perform well on the board examinations in Mathematics. Noticeably, most board examination questions are derived from NCERT textbooks. The NCERT book is therefore the most crucial tool for practising problems in Mathematics. However, Class 10 students may find it difficult to complete the NCERT exercises on their own. NCERT Solutions, such as the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1, might be useful in these situations. To complete the chapter and receive higher grades, students must be able to solve every problem in the Class 10 Maths Chapter 7 Exercise 7.1. Although these problems might initially seem challenging, with practise they will become simpler to resolve. The Extramarks learning platform can assist students who have difficulty understanding questions by helping them comprehend them better and solve the questions more quickly.Students can use the Extramarks learning platform to access a wide range of instructional modules and a wealth of study resources, including the NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.1, to meet their demands during board examination preparation.The NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 on the Extramarks website concentrate on a single chapter. These solutions serve as a useful tool for learning, practising, and answering questions. The fact that the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 from Extramarks have been created and compiled by experienced subject specialists ensures that all students will have a great learning experience.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry (Ex 7.1) Exercise 7.1

The most crucial method for getting ready for board examinations is solving NCERT exercises. Hence, it is typically advised that students practise the NCERT textbook questions. In order to verify their answers, they also need the right answers to the questions. Through NCERT Solutions, students may be able to receive the help they need when preparing for board examinations. They can apply the concepts from the lesson in a more simple and in-depth manner by using the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Thorough and error-free NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 are authored by highly qualified teachers. As a result, these solutions have been developed with consideration for the requirements and demands of Class 10 students. Solutions to the problems in the NCERT textbook have been divided into smaller, more manageable steps in order to make writing solutions easier. Teachers emphasise how crucial it is to give thorough, step-by-step answers in the examinations. In order to achieve the best results, students should carefully follow the instructions in the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1.

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Understanding the many concepts covered in the Class 10 Mathematics curriculum depends on getting the right instruction. Students can get NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 as well as other forms of assistance in order to fully comprehend the concepts in Chapter 7 of Mathematics. Students can obtain the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 on the Extramarks digital learning portal to assist with their preparation for the examinations. Students can gain confidence in their study strategy for the approaching examinations with the help of these study resources. To help students get ready for the board examinations, Class 10 includes a number of assessments as a part of the prescribed academic curriculum of the NCERT. However, in order to perform well on board examinations, students require appropriate guidance. Examination preparation could be enhanced by having access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 on the Extramarks educational website.

Chapter 7 Exercise 7.1: Topics Covered

Chapter 7 is based on a crucial concept in Mathematics called Coordinate Geometry. This chapter includes concepts that provide more details on some concepts that students have learned in Class 9. By studying this chapter, students will be able to find the distance between two points whose coordinates are known using the distance formula. Class 10 Maths Ch 7 Ex 7.1 covers the topic of Distance Formula. There are 10 questions in this exercise that involve finding the distance between two points. Students can refer to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 while solving this exercise to learn how to approach the questions in this exercise. Students also learn the section formula and area of a triangle in this chapter. They can learn the method of finding the area of a triangle formed by three given points. They can also learn to find the coordinates of the point that divides a line segment joining two points in a given ratio. Students should thoroughly read all these concepts and practise questions pertaining to them. This will not only help them score better marks in the board examinations but also help them in their future studies as well.

How Will the Solutions Be Helpful?

Students might not always have access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Although it is necessary, having a connection to the internet may not always be possible. Hence, students should have offline access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 in PDF format if they intend to continue their studies without hindrance. Every student’s educational demands are met by Extramarks. On the Extramarks website and Learning App, the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 are accessible in PDF format. Additionally, it is simple for students to download the PDF file and answer the questions whenever they require it without needing an internet connection. An all-inclusive answer to a student’s educational needs is provided by Extramarks. Although NCERT textbooks are great study resources, it can be difficult for students to get reliable NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. The answers to the questions are given in the NCERT textbook at the end, but their in-depth explanations are not provided accordingly. Students must comprehend the methods used to arrive at the answers while responding to the questions. They are required to provide detailed answers in order to receive full marks for their responses. To address this concern, Extramarks provides NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1.

Access NCERT solution for Class 10 Maths Chapter 7 – Coordinate Geometry

There is no doubt that students will be able to better understand the problems presented in the NCERT textbook if they have access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Additionally, they will be well aware of the solutions and methods for solving each question. There are organised approaches to answering each of the questions in the NCERT textbook. The NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 are accessible on the Extramarks website and mobile application to aid students in gaining a comprehensive conceptual understanding of the chapter.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Exercise 7.1

The NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 on Extramarks are helpful to students in a variety of ways. By using the comprehensive, step-by-step solutions provided in the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1, students are able to overcome challenging problems. It is necessary to dissect challenging mathematical problems in order to solve them. The NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 contain the technique which can be used to do the same. They gain confidence and advance their understanding of the most challenging topics when they use the NCERT textbook. Students can evaluate themselves and their progress by comparing their responses to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Extramarks provides comprehensive and authentic NCERT Solutions, such as NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Even if there are numerous sites that provide these solutions, their veracity is still questioned. Due to the significance of board examinations, students must use dependable study resources. The study materials that Extramarks offers have been verified as authentic by qualified mentors. The detailed NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 and other exercises are explained in straightforward language. The correct organisation of the answers is taught to the students. They provide the best and most straightforward methods for solving problems.

In addition to working sincerely, students preparing for the board examinations need to prepare smartly. They must develop a systematic approach if they want to achieve extraordinary outcomes from their preparation. For each subject, they should construct a study schedule and try to follow it routinely. They should plan every step of their preparation in advance. First, they should go over the syllabus and carefully study each topic in line with it. While also reviewing the questions from the textbook, they should make notes on important points and formulas. The students must also attempt to answer each of the exercises’ questions independently. In order to get assistance, they can use Extramarks’ NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Furthermore, they must write down any formulas that appear in the questions. Also, they can write down the procedures they followed to answer the questions. Following that, the topics should be revised with a specific focus on any lacunae that they may have overlooked. Finally, they should practise taking mock tests to ensure that they understand the material. They can also solve sample question papers and past years’ papers that are available on Extramarks.

Students require access to a variety of questions as well as solutions that are well explained before taking the board examinations. The majority of question banks are based on problems from NCERT textbooks. It is simpler for students to respond to questions when they have access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. They learn the concepts more quickly as a result. Students who learn new things quickly and easily feel more prepared for any examination. Students also benefit from having more time to study while still being able to focus on other academic tasks. They can advance in their preparation by comprehending the methods taught in the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Despite the chapter’s somewhat difficult and complicated content, having access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 that are personalised to students’ needs can be a helpful study tool. Using these study aids will make learning Coordinate Geometry easier. In order to advance consistently while solving other papers or problems, students might practice by answering NCERT questions. Among the study materials that focus on the particular topic of Coordinate Geometry, the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 by Extramarks is highly commendable for its ingenuity and credibility. Students who want to do better on the board examinations can have access to a variety of learning modules and study materials at Extramarks, including chapter-wise worksheets and practise tests. It should be emphasised that Extramarks offers educational facilities for testing, practice, and learning in one convenient location. With Extramarks’ NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1, students are guaranteed to receive a flawless educational experience.

On Extramarks, students can study under several highly exceptional mentors who have decades of experience in a variety of subjects. They fully explain each topic using educational techniques that are centred on the use of interactive audio-visual media. In order to assist students with improving their marks and learning outcomes, Extramarks consistently emphasises key concepts as well as efficient and thorough learning. Extramarks brings the material from fundamental textbooks to life through images and animations. The teams that create 2D and 3D animations are proficient in simplifying ideas so that they are easy to understand and remember during web-based learning. Extramarks provides students with the opportunity to engage fully in their education and study in an engaging manner. For the purpose of assisting students in preparing for their board examinations, the Extramarks platform for online learning has painstakingly compiled  NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 and other exercises.

Along with the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1, Class 10 students studying for their board examinations can also acquire the NCERT Solutions Class 10 for all the other subjects. The NCERT Solutions Class 10 are available in both Hindi and English to better serve the needs of students who study  these two languages. NCERT Solutions for Class 12 are also available for Mathematics and all other subjects for students in Class 12 preparing for the Class 12 board examinations.Extramarks provides NCERT Solutions for Class 11 students in Mathematics and other disciplines.NCERT Solutions are available in Hindi and English for all subjects for students in other classes as well. Along with NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 9, and NCERT Solutions Class 6, students can find NCERT Solutions Class 10 on the Extramarks website and smartphone application. For students in primary schools, Extramarks also provides NCERT Solutions, including NCERT Solutions Class 5, NCERT Solutions Class 2, NCERT Solutions Class 4, NCERT Solutions Class 3 and NCERT Solutions Class 1 for the NCERT textbook series. Students can obtain the PDF of the Class 10 Maths Ex 7.1 Solutions from the Extramarks website and Learning App.

NCERT Solutions for Class 10 Maths Chapter 7 All Other Exercises

The chapter on Coordinate Geometry includes a total of four exercises. Exercise 7.1 includes questions based on the Distance Formula. There are 10 questions in this exercise. Students can refer to Extramarks’ NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 while solving the questions in this exercise. Exercise 7.2 is based on the Section Formula. There are 10 questions in this exercise. Exercise 7.3 includes 5 questions that are based on the Area of a Triangle. Students should remember all the formulas in this chapter to solve the questions. Exercise 7.4 is an optional exercise for students and includes eight questions. Students can refer to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 and the solutions to other exercises to get assistance in solving the problems in these exercises.

Q.1 Find the distance between following pairs of points:
(i) (2, 3), (4, 1)
(ii) (–5, 7), (–1, 3)
(iii) (a, b), (–a, –b)

Ans.

(i) Distance between the two points (x1, y1) and (x2, y2) is given by the expression x2−x12+y2−y12.Therefore, distance between points (2, 3) and (4, 1)           =4−22+1−32=4+4=22 units(ii) Distance between the two points (x1, y1) and (x2, y2) is given by the expression x2−x12+y2−y12.Therefore, distance between points (−5, 7) and (−1, 3)           =−5−(−1)2+7−32=16+16=42 units(iii) Distance between the two points (x1, y1) and (x2, y2) is given by the expression x2−x12+y2−y12.Therefore, distance between points (a, b) and (−a, −b)           =a−(−a)2+b−(−b)2=4a2+4b2=2a2+b2

Q.2 Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

Ans.

Distance between points (0, 0) and (36, 15)           =(0−36)2+(0−15)2=1296+225=1521=39  unitsYes, we can find the distance between the given towns A and B.Let town A be at (0, 0) and town B be at (36, 15). Then, as perabove calculation, distance between the two towns is 39  km.

Q.3 Determine if the points (1, 5), (2, 3) and (– 2, –11) are collinear.

Ans.

Let the given points are P(1, 5), Q(2, 3) and R(−2,  −11).Now, using distance formula we find distance between thesepoints i.e., PQ, QR and PR.Distance between points P(1, 5) and Q(2, 3)     =PQ=(1−2)2+(5−3)2=1+4=5Distance between points Q(2, 3) and R(−2,  −11)    =QR=(2+2)2+(3+11)2=16+196=212=253Distance between points P(1, 5) and R(−2,  −11)    =PR=(1+2)2+(5+11)2=9+256=265Now,           PQ+QR=5+253≠265=PRi.e., PQ+QR≠PRTherefore, points P(1, 5), Q(2, 3) and R(−2,  −11) arenot collinear.

Q.4 Check whether (5, –2), (6, 4) and (7, –2) are the vertices of an isosceles triangle.

Ans.

Let the given points are P(5, −2), Q(6, 4) and R(7,  −2).Now, using distance formula we find distance between thesepoints i.e., PQ, QR and PR.Distance between points P(5, −2) and Q(6, 4)     =PQ=(5−6)2+(−2−4)2=1+36=37Distance between points Q(6, 4) and R(7,  −2)    =QR=(6−7)2+(4+2)2=1+36=37Distance between points P(5, −2) and R(7,  −2)    =PR=(5−7)2+(−2+2)2=4+0=2Now,           PQ+QR=37+37≠2=PRi.e., PQ+QR≠PRTherefore, points P(5, −2), Q(6, 4) and R(7,  −2) arenot collinear. They form an isosceles triangle as lengths of sides PQ and QR are equal.

Q.5 In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.


Ans.

It is given that 4 friends are seated at the points A(3, 4),B(6, 7), C(9, 4) and D(6, 1).Now, using distance formula we find length of each sideof the quadrilatral ABCD and diagonals AC and BD.AB=6−32+7−42=9+9=18=32,BC=6−92+7−42=9+9=18=32,CD=9−62+4−12=9+9=18=32,DA=6−32+4−12=9+9=18=32,AC=9−32+4−42=36+0=6,BD=6−62+7−12=0+36=6.We see that sides AB, BC, CD and DA are equal in lengths.Also, diagonals AC and BD are equal.Therefore, quadrilateral ABCD is a square. Hence, Champais correct.

Q.6 Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (–1, –2), (1, 0), (–1, 2), (–3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, –4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Ans.

(i)Let the given points are A(−1, −2), B(1, 0), C(−1, 2) andD(−3, 0).Now, using distance formula we haveAB=(−1−1)2+(−2−0)2=4+4=22,BC=(1+1)2+(0−2)2=4+4=22,CD=(−1+3)2+(2−0)2=4+4=22,DA=(−1+3)2+(−2−0)2=4+4=22andAC=(−1+1)2+(−2−2)2=0+16=4,BD=(1+3)2+(0−0)2=16+0=4.We see that sides AB, BC, CD and DA are equal in lengths.Also, diagonals AC and BD are equal.Therefore, the given points form a square.(ii)Let the given points are A(−3, 5), B(3, 1), C(0, 3) andD(−1, −4).Now, using distance formula we haveAB=(−3−3)2+(5−1)2=36+16=52,BC=(3−0)2+(1−3)2=9+4=13,CD=(0+1)2+(3+4)2=1+49=52,DA=(−1+3)2+(−4−5)2=4+81=85We see that sides AB, BC, CD and DA are not equal.Therefore, the given points do not form a special quadrilateral. These points form a general quadrilateral.(iii)Let the given points are A(4, 5), B(7, 6), C(4, 3) and D(1, 2).Now, using distance formula we haveAB=(4−7)2+(5−6)2=9+1=10,BC=(7−4)2+(6−3)2=9+9=32,CD=(4−1)2+(3−2)2=9+1=10,DA=(4−1)2+(5−2)2=9+9=32andAC=(4−4)2+(5−3)2=0+4=2,BD=(7−1)2+(6−2)2=36+16=52.We see that opposite sides of quadrilateral ABCD are equal.But, diagonals AC and BD are not equal.Therefore, the given points form a parallelogram.

Q.7 Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

Ans.

Let T(x, 0) be the point on the x-axis which is equidistant fromA(2, −5) and B(−2, 9).Now, using distance formula we haveTA=(x−2)2+(0+5)2=x2−4x+4+25=x2−4x+29andTB=(x+2)2+(0−9)2=x2+4x+4+81=x2+4x+85Now, TA=TBor    x2−4x+29=x2+4x+85or    x2−4x+29=x2+4x+85or    8x=29−85=−56or    x=−7Hence, the required point is (−7, 0).

Q.8 Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.

Ans.

It is given that the distance between the points P(2, −3) and(10, y) is 10 units.Therefore, using distance formula we have        (2−10)2+(−3−y)2=10or    64+9+6y+y2=100or    y2+6y−27=0or    y2+9y−3y−27=0or    y(y+9)−3(y+9)=0or    (y−3)(y+9)=0or    y=3 or  y=−9

Q.9 If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR.

Ans.

It is given that Q(0, 1) is equidistant from P(5, −3) and R(x, 6). Therefore, using distance formula, we have        (0−5)2+(1+3)2=(0−x)2+(1−6)2or    25+16=x2+25or    x2=16or    x=±4When x=4, thenQR=(0−4)2+(1−6)2=41 unitsandPR=(5−4)2+(−3−6)2=82 unitsWhen x=−4,  thenQR=(0+4)2+(1−6)2=41 unitsandPR=(5+4)2+(−3−6)2=92 units

Q.10 Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (–3, 4).

Ans.

It is given that the point (x, y) is equidistant from thepoint (3, 6) and R(−3, 4).Therefore, using distance formula, we have        (x−3)2+(y−6)2=(x+3)2+(y−4)2or    x2−6x+9+y2−12y+36=x2+6x+9+y2−8y+16or   −6x−6x−12y+8y+45−25=0or    −12x−4y+20=0or    3x+y−5=0

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FAQs (Frequently Asked Questions)

1. Is it possible to find NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 on the Extramarks website?

The Extramarks website and mobile application both provide quick access to the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 in PDF format.

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3. Do the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 help in understanding the concepts covered in this chapter?

Students in Class 10 who are preparing for their board exams need to use NCERT solutions. To prepare for the board examination, students can use learning resources like the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1. Only giving answers will not be enough for students. They must familiarise themselves with the procedures used to get the result. Students may improve their potential to respond to each similar question that appears in the examination by becoming more proficient at following clear tactics and procedures.

4. Which chapter is covered in the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1?

The NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1 cover the chapter on Coordinate Geometry. The questions in this exercise are mainly based on the Distance Formula that is used to find the distance between two given points in the Cartesian plane.

5. What advantages do students gain from using the NCERT Solutions Class 10 Maths Chapter 7 Exercise 7.1?

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