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Imagine you're given three points in a plane and asked to find the area of the triangle they form. Instead of using traditional geometry formulas, determinants offer a powerful method to compute this area efficiently. Class 12 Maths Chapter 4 – Determinants, Exercise 4.2 of NCERT introduces the application of determinants in finding the area of a triangle when the coordinates of its vertices are known. This exercise enhances understanding of how algebraic concepts like determinants can be applied to solve geometric problems. This article on NCERT Solutions for Exercise 4.2 Class 12 Maths Chapter 4 - Determinants, offers clear and step-by-step solutions for the exercise problems.
As per the reports, the Central Board of Secondary Education (CBSE) will declare the Class 10, 12 board exams 2025 in the mid-May on its official website at cbse.gov.in and results.cbse.nic.in. Notably, students will also be able to check their marks through Digilocker with the help of access codes.
Question:1(i) Find area of the triangle with vertices at the point given in each of the following :
Answer:
We can find the area of the triangle with vertices
Expanding using second column
Question:1(ii) Find area of the triangle with vertices at the point given in each of the following :
Answer:
We can find the area of the triangle with given coordinates by the following method:
Question:1(iii) Find area of the triangle with vertices at the point given in each of the following :
Answer:
Area of the triangle by the determinant method:
Hence the area is equal to
Question:2 Show that points
Answer:
If the area formed by the points is equal to zero then we can say that the points are collinear.
So, we have an area of a triangle given by,
calculating the area:
Hence the area of the triangle formed by the points is equal to zero.
Therefore given points
Question:3(i) Find values of k if area of triangle is 4 sq. units and vertices are
Answer:
We can easily calculate the area by the formula :
or
Hence two values are possible for k.
Question:3(ii) Find values of k if area of triangle is 4 sq. units and vertices are
Answer:
The area of the triangle is given by the formula:
Now, calculating the area:
or
Therefore we have two possible values of 'k' i.e.,
Question:4(i) Find equation of line joining
Answer:
As we know the line joining
Therefore area formed by them will be equal to zero.
So, we have:
or
Hence, we have the equation of line
Question:4(ii) Find equation of line joining
Answer:
We can find the equation of the line by considering any arbitrary point
So, we have three points which are collinear and therefore area surrounded by them will be equal to zero.
Calculating the determinant:
Hence we have the line equation:
Question:5 If the area of triangle is 35 sq units with vertices
(A)
Answer:
Area of triangle is given by:
or
Hence the possible values of k are 12 and -2.
Therefore option (D) is correct.
Also read,
Here are the main topics covered in NCERT Class 12 Chapter 4, Determinants: Exercise 4.2:
1. Area of a Triangle Using Determinants:
Given the coordinates of the vertices of a triangle as
Area
This formula utilizes the determinant of a
2. Collinearity of Points:
If the area calculated using the above determinant is zero, it implies that the three points are collinear, i.e., they lie on a straight line and do not form a triangle.
Also, read,
Given below are some useful links for subject-wise NCERT solutions of class 12.
Here are some links to subject-wise solutions for the NCERT exemplar class 12.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Yes, we can find the area of the triangle using determinants if the vertices of the triangle are given.
Yes, here you will get NCERT Solutions for free. NCERT solutions for Class 12 Maths, Physics, Chemistry and Biology are available chapter wise.
Yes, You can download the NCERT book from their official website.
Here you will get NCERT Solutions for Class 6 to 10. The solutions for Science and Mathematics are given chapter wise. Students can follow NCERT syllabus for a better score to get good marks in CBSE annual exams.
Triangle formed by three collinear points is a straight line, hence the area of such a triangle is zero.
NCERT solutions are useful for the students to get conceptual clarity.
NCERT solutions are helpful for competitive exams like JEE Main, NEET, VITEEE, etc.
There are 13 chapters starting from relations and functions to probability. Chapters from algebra, calculus are present.
Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.
Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
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