NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry (Ex 7.3) Exercise 7.3
Home > NCERT Solutions > NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry (Ex 7.3) Exercise 7.3

CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
NCERT provides indepth knowledge of various subjects through the books they publish. However, books are not the only educational material provided by NCERT. NCERT, or the National Council of Educational Research and Teaching, is an organisation formed by the government to provide educational materials and teaching materials to schools. Many schools have been affiliated with NCERT in order to train new teachers and give educational resources to their students. The resources given by NCERT are widely used by students to prepare for many exams, like the board exams for Class 10 and Class 12, and various entrance exams like JEE, NEET, CUET, NDA, etc., for admission into different programmes and universities of theirdesire.
For some students, Mathematics is a particularly tricky subject. They might have trouble with Mathematics, and they might run into trouble with some problems. Mathematics has always piqued the curiosity of students. Geometry is new to all students and may scare them even if Algebra, Trigonometry, and Linear Equations in Two Variables are all included in Mathematics for Class 9 and Class 10. While some students struggle with it, others relish the challenges. Students may find it more difficult to finish the NCERT Exercises because they may find it challenging to comprehend the themes when they are studying them for the first time. Even though learning something new is never simple, after they have mastered it, they will feel incredibly satisfied when they are done with their studies. Understanding and studying the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 is important, and it takes a lot of practice. Students can better understand all of the chapter’s topics with the guidance of the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3.
The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 provide information about the topics in Class 10 Maths Chapter 7 Exercise 7.3. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 provides the solutions to the questions given in Class 10 Maths Ex 7.3. These NCERT Solutions are helpful for students. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 is a resourceful tool as it provides students with the resources to solve the questions given in the books published by NCERT. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 will help students understand the chapter and find out the correct answers and methods of answering each question.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry (Ex 7.3) Exercise 7.3
To effectively manage their time during an exam, students must be able to quickly solve a question. Time management during the exam is crucial for students since it will enable them to review their answer sheets at the end and check for any major errors. Answering the questions requires thoroughly reviewing the materials provided to students and then figuring out the method of solution and formula, at the end, proper implementation is necessary to get the correct answers. This gives them time to remedy their errors while also assisting them in understanding how they should have answered the questions and where they must have gone wrong. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 can assist students in recognising and fixing their errors when practising, as well as becoming aware of several mistakes they are prone to make during the exam due to pressure and anxiety Hence, The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 is quite useful during taking exams. It will assist the students in time management during the exam, completion of their coursework, and preparation for the test.
Extramarks is an educational platform that provides both online and offline courses along with study material. With the help of Extramarks, students can learn in a flexible environment. Students have the option of receiving help offline or online. As it is explained in NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3, students can obtain academic support for any subject they want in any language they wish to learn in, depending on their needs. Students can find out more about Extramarks on their website and mobile application. Students can look for other resources and test education material available by going through Extramarks’ website and application. They will find it easier to study and prepare for exams when they use the material provided to them by Extramarks through their online portal.
Access NCERT Solutions for Maths Chapter 7 – Coordinate Geometry
NCERT has been employed to teach the foundations of Mathematics and other topics ever since it began. NCERT is one of the best books to prepare for achieving higher marks on the CBSE board exams. NCERT books are a part of the curriculum for many students whose schools are affiliated with CBSE, or the Central Board of Secondary Education. CBSE has been recommending the NCERT books for study. The Mathematics NCERT book is one of the suggested textbooks for board exams. Most students prioritise solving NCERT problems before working on practise papers or taking a test. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 will be helpful to students as they progress through the NCERT. They can use the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 to quickly get the correct answers or faster solutions to these problems.
Students will have a thorough understanding of the question and how to solve it after completing the NCERT questions.. They will acquire the skills necessary to solve new issues from other textbooks or to take exams to have their abilities evaluated and any flaws found by having studied NCERT. They can fill up their knowledge and ability gaps by repeatedly responding to questions and by using the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3. Students must seek help if they find a topic difficult, feel that their answer might be flawed, or anticipate that it will take too long to solve. Instead, if they think the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 may provide them with a better understanding, they should go through the solutions for a thorough understanding.
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Exercise 7.3
Students must practise Chapter 7 Coordinate Geometry in order to gain good marks in their exams. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 will students gain a thorough understanding of the chapter.The Class 10 Maths Exercise 7.3 Solutions by Extramarks is an epic tool for students to use in their preparation for getting good scores in exams. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 also gives an overview of the chapter to students to help them understand and draw rough sketches of the concepts that will be presented to them in the chapter. The concepts that are included in this chapter, as mentioned in the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 are the use of the distance formula, the section formula, the midpoint formula and the area of a triangle. This helps students understand the application of these formulas of geometry in various different types of questions. This will help them solve more advanced problems. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 will help students understand the basic concepts from NCERT and help them solve advanced questions. In addition to these topics and exercises based on them, NCERT textbooks like the Exemplar also have optional exercises available to them for studying advanced questions that contain questions where more than one formula or concept might need to be applied. These exercises will help them solve that.
Students will find plenty of study resources on Extramarks’ website, including the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3. There are study materials accessible for limited assistance. For additional information and help, students can find NCERT solutions for a variety of classes and disciplines at different levels. NCERT Solutions Class 12 and NCERT Solutions Class 11 are accessible to students pursuing upper secondary education. These solutions are available for courses like Physics, Biology, Mathematics, Chemistry, Business Studies, Economics, Hindi, and English for senior secondary students. The NCERT Solutions Class 9 and NCERT Solutions Class 10 are available to secondary school students. These secondary school students’ solutions are available for courses like Science, Math, Social Studies, Hindi and English. The NCERT Solutions Class 6, NCERT Solutions Class 7, and NCERT Solutions Class 8 are available to middle school students on the Extramarks website and mobile app. These middle school students’ answers can be found for subjects including Science, Mathematics, Social Sciences, English, and Hindi. Students in schools receiving primary education have access to NCERT Solutions Class 1, NCERT Solutions Class 2, NCERT Solutions Class 3, NCERT Solutions Class 4, and NCERT Solutions Class 5. For topics like Mathematics, EVS, Hindi, and English, these primary school solutions for NCERT books are available. Students can use the NCERT Solutions for Class 10 Maths, Chapter 7, Exercise 7.3, to get a general understanding of the solutions provided by Extramarks.
The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 might help students become aware of their errors in problemsolving. It is crucial that students understand that making mistakes is common and that they should instead view them as learning opportunities. By reading through the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 once, the chapter will also be reviewed in preparation for the test. Although their initial response might be incorrect, they can improve it with enough practice, the proper formula, and the appropriate technique. They will benefit from the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3. Their study time will be more effective if they take appropriate pauses to rest. Students may be more motivated to study for a long time until the test if they are happy and healthy. Students who are uncertain about their exam preparation may consequently find value in the study materials from Extramarks.
Extramarks provides doubt sessions to help those who are confused with any questions or concepts. Students can access the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 for a better conceptual understanding. If students choose to take mock exams and receive feedback on how they performed, it will be very helpful for them to learn how they could improve their work. Students can prepare through Extramarks, which will assist them in synchronising their syllabus with Extramarks’ academic schedule. The NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 can be scrutinised by the students. Therefore, students must consider the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 during their revision period. Students can use these solutions to examine the correct responses before an exam and check their solutions for faults. Students may find the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 to be of great assistance throughout their preparation. Students must make the most of all of their resources to improve themselves and understand their strengths and weaknesses so they can adjust their approaches to different questions and plan their academic learning accordingly. All of this can encourage a student to do well on examinations and earn good marks.
Q.1
$\begin{array}{l}\text{Find the area of the triangle whose vertices are :}\\ \text{(i) (}2,\text{}3),\text{}(1,\text{}0),\text{}(2,4)\\ \text{(ii)}(5,\text{}1),\text{}(3,\text{}5),\text{}(5,\text{}2)\end{array}$
Ans
$\begin{array}{l}\text{Area of a triangle with vertives (}{\mathrm{x}}_{1}{\text{, y}}_{1}\text{), (}{\mathrm{x}}_{2}\text{,}{\mathrm{y}}_{2}\text{) and (}{\mathrm{x}}_{3}\text{,}{\mathrm{y}}_{3}\text{)}\\ \text{is given by the expression}\frac{1}{2}\left\{{\mathrm{x}}_{1}({\mathrm{y}}_{2}{\mathrm{y}}_{3})+{\mathrm{x}}_{2}({\mathrm{y}}_{3}{\mathrm{y}}_{1})+{\mathrm{x}}_{3}({\mathrm{y}}_{1}{\mathrm{y}}_{2})\right\}\text{.}\\ \text{Therefore,}\\ \text{(i) Area of the triangle with vertices (}2,\text{}3),\text{}(1,\text{}0\left)\text{and}\right(2,4)\\ \text{}=\frac{1}{2}\left\{2(0(4\left)\right)+(1)(43)+2(30)\right\}\\ \text{}=\frac{1}{2}(8+7+6)=\frac{21}{2}\text{square units}\\ \text{(ii) Area of the triangle with vertices}(5,\text{}1),\text{}(3,\text{}5)\text{and}(5,\text{}2)\\ \text{}=\frac{1}{2}\left\{5(52)+3(2(1\left)\right)+5(1(5)\right\}\\ \text{}=\frac{1}{2}(35+9+20)=32\text{square units}\end{array}$
Q.2 In each of the following find the value of ‘k’, for which the points are collinear.
(i) (7, –2), (5, 1), (3, k)
(ii) (8, 1), (k, – 4), (2, –5)
Ans
$\begin{array}{l}\text{Points (}{\mathrm{x}}_{1}{\text{, y}}_{1}\text{), (}{\mathrm{x}}_{2}\text{,}{\mathrm{y}}_{2}\text{) and (}{\mathrm{x}}_{3}\text{,}{\mathrm{y}}_{3}\text{) are collinear if}\\ \frac{1}{2}\left\{{\mathrm{x}}_{1}({\mathrm{y}}_{2}{\mathrm{y}}_{3})+{\mathrm{x}}_{2}({\mathrm{y}}_{3}{\mathrm{y}}_{1})+{\mathrm{x}}_{3}({\mathrm{y}}_{1}{\mathrm{y}}_{2})\right\}=0\\ \text{Therefore,}\\ \text{(i) Points (7,}\text{2)},\text{(5, 1) and (3, k) are collinear if}\\ \text{}\frac{1}{2}\left\{7(1\mathrm{k})+5(\mathrm{k}+2)+3(21)\right\}=0\\ \text{or 7}\text{7}\mathrm{k}+5\mathrm{k}+109=0\\ \text{or}\text{2k}+\text{8}=0\\ \text{or}\mathrm{k}=4\\ \text{(ii) Points (8, 1)},\text{(}\mathrm{k}\text{,}4\text{) and (2,}5\text{) are collinear if}\\ \text{}\frac{1}{2}\left[8\{4(5\left)\right\}+\mathrm{k}(51)+2\{1(4\left)\right\}\right]=0\\ \text{or 8}6\mathrm{k}+10=0\\ \text{or}\text{6k}=1\text{8}\\ \text{or}\mathrm{k}=3\text{}\end{array}$
Q.3
$\begin{array}{l}\text{Find the area of the triangle formed by joining the}\\ \text{midpoints of the sides of the triangle whose}\\ \text{vertices are}(0,\text{}1),\text{}(2,\text{}1)\text{and (0, 3). Find the}\\ \text{ratio of this area to the area of the given triangle.}\end{array}$
Ans
$\begin{array}{l}\text{Area of a triangle with vertices (}{\mathrm{x}}_{1}{\text{, y}}_{1}\text{), (}{\mathrm{x}}_{2}\text{,}{\mathrm{y}}_{2}\text{) and (}{\mathrm{x}}_{3}\text{,}{\mathrm{y}}_{3}\text{)}\\ \text{is given by the expression}\frac{1}{2}\left\{{\mathrm{x}}_{1}({\mathrm{y}}_{2}{\mathrm{y}}_{3})+{\mathrm{x}}_{2}({\mathrm{y}}_{3}{\mathrm{y}}_{1})+{\mathrm{x}}_{3}({\mathrm{y}}_{1}{\mathrm{y}}_{2})\right\}\text{.}\\ \text{Therefore,}\\ \text{area of the triangle with vertices (0},\text{}1),\text{}(2,\text{1}\left)\text{and}\right(0,3)\\ \text{}=\frac{1}{2}\left\{0(13)+2(3+1)+0(11)\right\}\\ \text{}=\frac{1}{2}(0+8+0)=4\text{square units}\\ \text{Vertices of the triangle formed by joining the midpoints of the}\\ \text{sides of the triangle with vertices}(0,\text{}1),\text{}(2,\text{}1)\text{and (0, 3)}\\ \text{are}(\frac{0+2}{2},\text{}\frac{1+1}{2}),\text{}(\frac{2+0}{2},\text{}\frac{1+3}{2})\text{and}(\frac{0+0}{2},\text{}\frac{1+3}{2})\text{i.e.,}\\ (1,\text{}0),\text{}(1,\text{}2)\text{and}(0,\text{}1).\\ \text{Area of the triangle with vertices}(1,\text{}0),\text{}(1,\text{}2)\text{and}(0,\text{}1)\\ \text{}=\frac{1}{2}\left\{1(21)+1(10)+0(02)\right\}\\ \text{}=\frac{1}{2}(1+1+0)=1\text{square unit}\\ \text{Therefore, required ratio}=1:4\text{}\end{array}$
Q.4
$\begin{array}{l}\text{Find the area of the quadrilateral whose vertices, taken in order, are (}\text{4,}\text{2), (}\text{3,}\text{5), (}3,\text{}2\text{)}\\ \text{and (2, 3).}\end{array}$
Ans
\begin{array}{l}\text{Area of a triangle with vertices (}{x}_{1}{\text{, y}}_{1}\text{), (}{x}_{2}\text{,}{y}_{2}\text{) and (}{x}_{3}\text{,}{y}_{3}\text{)}\\ \text{is given by the expression}\frac{1}{2}\left\{{x}_{1}({y}_{2}{y}_{3})+{x}_{2}({y}_{3}{y}_{1})+{x}_{3}({y}_{1}{y}_{2})\right\}\text{.}\\ \text{Therefore,}\\ \text{area of}\Delta \text{ABC with vertices A(}4,\text{}2),\text{B(}3,\text{}5)\text{and C(3,}2)\\ \text{}=\frac{1}{2}\left\{4(5+2)+(3)(2+2)+3(2+5)\right\}\\ \text{}=\frac{1}{2}(12+0+9)=\frac{21}{2}\text{square units}\\ \text{area of}\Delta \text{ADC with vertices A(}4,\text{}2),\text{D(2},\text{3})\text{and C(3,}2)\\ \text{}=\frac{1}{2}\left\{4(3+2)+2(2+2)+3(23)\right\}\\ \text{}=\frac{1}{2}(20+015)=\frac{35}{2}\text{}\\ \text{But area is always a positive quantity}\text{.}\\ \therefore \text{area of}\Delta \text{ADC}=\frac{35}{2}\text{square units}\\ \text{Area of the given quadrilateral ABCD}\\ \text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}=\text{area of}\Delta \text{ABC}+\text{area of}\Delta \text{ADC}\\ \text{\hspace{0.17em}}\text{}\text{\hspace{0.17em}}=\left(\frac{21}{2}+\frac{35}{2}\right)\text{square units}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}=\text{28 square units}\end{array}
Q.5
$\begin{array}{l}\mathrm{You}\text{\hspace{0.17em}}\mathrm{have}\text{\hspace{0.17em}}\mathrm{studied}\text{\hspace{0.17em}}\mathrm{in}\text{\hspace{0.17em}}\mathrm{Class}\text{\hspace{0.17em}}\mathrm{IX},\text{\hspace{0.17em}}\left(\mathrm{Chapter}\text{\hspace{0.17em}}9,\text{\hspace{0.17em}}\mathrm{Example}\text{\hspace{0.17em}}3\right),\\ \mathrm{that}\text{\hspace{0.17em}}\mathrm{a}\text{\hspace{0.17em}}\mathrm{median}\text{\hspace{0.17em}}\mathrm{of}\text{\hspace{0.17em}}\mathrm{a}\text{\hspace{0.17em}}\mathrm{triangle}\text{\hspace{0.17em}}\mathrm{divides}\text{\hspace{0.17em}}\mathrm{it}\text{\hspace{0.17em}}\mathrm{into}\text{\hspace{0.17em}}\mathrm{two}\text{\hspace{0.17em}}\mathrm{triangles}\\ \mathrm{of}\text{\hspace{0.17em}}\mathrm{equal}\text{\hspace{0.17em}}\mathrm{areas}.\text{\hspace{0.17em}}\mathrm{Verify}\text{\hspace{0.17em}}\mathrm{this}\text{\hspace{0.17em}}\mathrm{result}\text{\hspace{0.17em}}\mathrm{for}\text{\hspace{0.17em}}\mathrm{\Delta ABC}\text{\hspace{0.17em}}\mathrm{whose}\\ \mathrm{vertices}\text{\hspace{0.17em}}\mathrm{are}\text{\hspace{0.17em}}\mathrm{A}\left(4,6\right),\text{\hspace{0.17em}}\mathrm{B}\left(3,2\right)\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\mathrm{C}\left(5,2\right).\end{array}$
Ans
$\begin{array}{l}\text{Area of a triangle with vertives (}{\mathrm{x}}_{1}{\text{, y}}_{1}\text{), (}{\mathrm{x}}_{2}\text{,}{\mathrm{y}}_{2}\text{) and (}{\mathrm{x}}_{3}\text{,}{\mathrm{y}}_{3}\text{)}\\ \text{is given by the expression}\frac{1}{2}\left\{{\mathrm{x}}_{1}({\mathrm{y}}_{2}{\mathrm{y}}_{3})+{\mathrm{x}}_{2}({\mathrm{y}}_{3}{\mathrm{y}}_{1})+{\mathrm{x}}_{3}({\mathrm{y}}_{1}{\mathrm{y}}_{2})\right\}\text{.}\\ \text{Therefore,}\\ \text{area of}\mathrm{\Delta}\text{ABC with vertices A(}4,\text{}6),\text{B(}3,\text{}2)\text{and C(5,}2)\\ \text{}=\frac{1}{2}\left\{4(22)+3(2+6)+5(6+2)\right\}\\ \text{}=\frac{1}{2}(16+2420)=6\text{}\\ \text{But area is always a positive quantity.}\\ \therefore \text{area of}\mathrm{\Delta}\text{ABC}=6\text{square units}\\ \text{Now, D is the midpoint of BC. Therefore, coordinates of D are}\\ (\frac{3+5}{2},\text{}\frac{2+2}{2})\text{i.e., (4, 0).}\\ \text{area of}\mathrm{\Delta}\text{ADC with vertices A(}4,\text{}6),\text{D(4},\text{0})\text{and C(5,}2)\\ \text{}=\frac{1}{2}\left\{4(02)+4(2+6)+5(6+0)\right\}\\ \text{}=\frac{1}{2}(8+3230)=3\\ \text{But area is always a positive quantity.}\\ \therefore \text{area of}\mathrm{\Delta}\text{ADC}=3\text{square units}\\ \text{area of}\mathrm{\Delta}\text{ABD with vertices A(}4,\text{}6),\text{B(3,}2)\text{and D(4},\text{0})\\ \text{}=\frac{1}{2}\left\{4(20)+3(0+6)+4(6+2)\right\}\\ \text{}=\frac{1}{2}(8+1816)=3\\ \text{But area is always a positive quantity.}\\ \therefore \text{area of}\mathrm{\Delta}\text{ABD}=3\text{square units}\\ \text{Now, we observe that}\\ \text{area of}\mathrm{\Delta}\text{ADC}=\text{area of}\mathrm{\Delta}\text{ABD}=3\text{square units}\\ \text{Hence, we verified the result}\mathbf{that}\text{}\mathbf{a}\text{}\mathbf{median}\text{}\mathbf{of}\text{}\mathbf{a}\text{}\mathbf{triangle}\text{}\mathbf{divides}\\ \mathbf{it}\text{}\mathbf{into}\text{}\mathbf{two}\text{}\mathbf{triangles}\text{}\mathbf{of}\text{}\mathbf{equal}\text{}\mathbf{areas}.\end{array}$
Please register to view this section
FAQs (Frequently Asked Questions)
1. With the use of the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3, how can students enhance their performance?
Students are conscious of the fact that consistent study is necessary to prepare for any exam. They can stay on schedule with the aid of the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3. Students can lessen the foolish errors they make on assessments by studying and practising. After some practice, students will better understand all the concepts, and once they have mastered it, it will be easier for them to apply them to problems from related or unrelated topics and chapters. A great example of this is the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3.
2. Why do students find NCERT Class 10 Maths Chapter 7 Exercise 7.3 difficult to solve? How does that relate to the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3?
When attempting to solve problems, it is typical to run across doubts. It is difficult to properly understand and apply the formulas accurately on the first try. Students can ask for help from their teachers, peers, and the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3 to advance in their studies. The students must keep in mind that while it may initially take them some time to properly understand the concepts and facts, studying will unquestionably make them better. They can take help from learning tools like the NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.3.