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NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2 Determinants - PDF Download

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NCERT solutions for class 12 maths chapter 4 exercise 4.2 Determinants have explained the concept of calculating the area of a triangle using determinants. Determinants can be used to calculate and express the area of a triangle whose vertices are known. The area of the triangle formed by using three collinear points is zero. NCERT solutions for class 12 maths chapter 4 ex 4.3 have interactive illustrations that are a great way to enhance computational skills. 

Ex 4.2 class 12 maths chapter 4 consists of 5 questions that are solved with a step by step method to find the area of the triangle. The Questions given in this exercise are effective in providing a clear understanding of how to use the method to find the answers. Class 12 maths chapter 4 exercise 4.2 NCERT solutions are prepared by subject experts of eSaral to help you score good marks in board exams. You can also download these solutions in PDF format. This will help you to gain detailed knowledge of the topic mentioned above with solved questions. Download the free PDF of NCERT solutions for ex 4.2 class 12 maths chapter 4 from the official website of eSaral.

Topics Covered in Exercise 4.2 Class 12 Mathematics Questions

Ex 4.2 class 12 maths ch 4 is completely based on the topic of area of triangle. This topic is elaborated in a detailed manner here by expert teachers of eSaral that you can check below.

1.

Area of a Triangle

  1. Area of a Triangle

When the coordinates of the triangle's vertices are known, the area of the triangle can be found using the formula for area of a triangle in determinant form. The area of triangle in determinant Form is the name given to this formula since it makes use of the determinant concepts.

Let say, we have the area of a triangle whose vertices are (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ), is given by the expression $\frac{1}{2}$ [x1(y2 –y3) + x2(y3 –y1) + x3(y1 –y2)]. Now this expression can be written in the form of a determinant as

             $\Delta=\frac{1}{2}\left|\begin{array}{lll}x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1\end{array}\right|$

(i) If area is given, use both positive and negative values of the determinant for calculation.

(ii) The area of the triangle formed by three collinear points is zero.

Tips for Solving Exercise 4.2 Class 12 Chapter 4 Determinants

Ex 4.2 class 12 maths ch 4 helps in practicing questions based on area of triangle. Here, our academic team of mathematics have provided some useful tips to solve ex 4.2 questions with ease.

  1. By going over every concept in NCERT solutions and practicing the questions thoroughly, students will be able to build the proper strategy to perform in-depth learning.

  2. Students should first solve easy questions of exe 4.2 then move on to complex questions to form a clear understanding of topics.

  3. Students must remember the formula to find the area of a triangle in ex 4.2 class 12 maths ch 4.

Importance of Solving Ex 4.2 Class 12 Maths Chapter 4 Determinants

NCERT solutions class 12 maths chapter 4 ex 4.2 has many benefits of solving questions. Some of the benefits are provided below by expert faculties of eSaral.

  1. Ex 4.2 class 12 maths ch 4 NCERT solutions included questions based on area of triangle that has been explained in precise and step by step manner.

  2. By practicing ex 4.2 class 12 maths questions will eliminate errors while solving the questions in exams.

  3. NCERT solutions class 12 maths chapter 4 ex 4.2 also includes examples and important questions related to area of triangle that will help you to build conceptual knowledge of the topic.

  4. You can cross-check your answers by going through the NCERT solutions PDFs.

Frequently Asked Questions 

Question 1. What is the formula to find the area of a triangle using determinants?

Answer 1. The area of a triangle using determinants is given below.

Area of triangle = $\frac{1}{2}\left|\begin{array}{lll}x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1\end{array}\right|$

Question 2. Can I get the NCERT solutions for class 12 maths chapter 4 ex 4.2?

Answer 2. Yes, you can get the free NCERT solutions for class 12 maths chapter 4 ex 4.2 from eSaral website. 

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