Find the best tutors and institutes for Class 12 Tuition
Q3(ii):
Find values of $k$ if area of triangle is 4 sq. units and vertices are (ii) $(–2, 0), (0, 4), (0, k)$
Solution :
Step 1: Theoretical Foundation for Area of a Triangle
The area of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is defined by the determinant formula [Per the Coordinate Geometry definition of area]:
$\text{Area} = \frac{1}{2} \left| \det \begin{pmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{pmatrix} \right|$
Step 2: Substituting Given Coordinates
Given vertices: $(x_1, y_1) = (-2, 0)$, $(x_2, y_2) = (0, 4)$, $(x_3, y_3) = (0, k)$.
Given Area = $4$ sq. units. Therefore:
$4 = \frac{1}{2} \left| \det \begin{pmatrix} -2 & 0 & 1 \\ 0 & 4 & 1 \\ 0 & k & 1 \end{pmatrix} \right|$
$8 = \left| \det \begin{pmatrix} -2 & 0 & 1 \\ 0 & 4 & 1 \\ 0 & k & 1 \end{pmatrix} \right|$ [By multiplying both sides by 2]
Step 3: Evaluating the Determinant
Expanding the determinant along the first column (Column 1) for computational efficiency [By Laplace Expansion]:
$\det = -2 \begin{vmatrix} 4 & 1 \\ k & 1 \end{vmatrix} - 0 \begin{vmatrix} 0 & 1 \\ k & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 4 & 1 \end{vmatrix}$
$\det = -2(4(1) - k(1)) - 0 + 0$
$\det = -2(4 - k)$
$\det = -8 + 2k$
Step 4: Solving for $k$
Since the determinant is within an absolute value sign, we must account for both positive and negative scenarios [By the Definition of Absolute Value]:
$|2k - 8| = 8$
Case 1:
$2k - 8 = 8$
$2k = 16 \implies k = 8$
Case 2:
$2k - 8 = -8$
$2k = 0 \implies k = 0$
Visual Representation of Triangle Vertices
Final Solution: The values of $k$ are $0$ and $8$.
More Questions from Class 12 Mathematics Determinants EXERCISE 4.2
- Q1(i): Find area of the triangle with vertices at the point given in each of the following: (i) $(1, 0), (6, 0), (4, 3)$
- Q1(ii): Find area of the triangle with vertices at the point given in each of the following: (ii) $(2, 7), (1, 1), (10, 8)$
- Q1(iii): Find area of the triangle with vertices at the point given in each of the following: (iii) $(–2, –3), (3, 2), (–1, –8)$
- Q2: Show that points A $(a, b + c)$, B $(b, c + a)$, C $(c, a + b)$ are collinear.
- Q3(i): Find values of $k$ if area of triangle is 4 sq. units and vertices are (i) $(k, 0), (4, 0), (0, 2)$
- Q4(i): (i) Find equation of line joining $(1, 2)$ and $(3, 6)$ using determinants.
- Q4(ii): (ii) Find equation of line joining $(3, 1)$ and $(9, 3)$ using determinants.
- Q5: If area of triangle is 35 sq units with vertices $(2, – 6), (5, 4)$ and $(k, 4)$. Then $k$ is
CBSE Solutions for Class 12 Mathematics Determinants
Chapters in CBSE - Class 12 Mathematics
Top Tutors who teach Determinants
Super Tutor
Bilekahalli, Bangalore
6 yrs of
Exp
9 students
326 hrs of classes completed
500
per hour
Online Classes
I teach Chemistry to students of Class 11 and Class 12 and have been working in the teaching field for the past 7 years. Chemistry has always been a subject that I am passionate about, and I enjoy helping students understand concepts clearly and perform confidently in academics as well as competitive examinations. My goal is to make Chemistry simple, logical, and interesting for students through structured and concept-focused learning. I hold a Master of Science (M.Sc.) degree in Chemistry, which has provided me with strong subject knowledge and a deeper understanding of various chemical concepts. My academic background helps me explain topics in a clear and systematic way so that students can easily understand and apply them while solving numerical and theoretical questions. Over the years, I have worked with students from different learning backgrounds and understanding levels. This experience has taught me the importance of adapting teaching methods according to the student’s requirements. I focus on helping students strengthen their conceptual understanding, improve their analytical and problem-solving skills, and gain confidence in handling Chemistry effectively for both board exams and competitive exams. My teaching methodology is structured, student-centric, and exam-oriented. I follow a well-planned lesson structure where topics progress step by step from basic to advanced levels. Before starting a new topic, I assess the student’s current understanding level so that I can explain concepts in the most effective manner. I also use suitable real-life examples to simplify complex chemical concepts and make learning more relatable and easier to understand. I strongly believe that conceptual clarity is more important than rote learning. During my classes, I encourage students to ask questions freely and clear doubts without hesitation. If a student finds a concept difficult, I patiently re-explain it multiple times until complete understanding is achieved. I also conduct regular revision sessions, exercise practice, and detailed discussions of previous years’ board and competitive examination questions to strengthen preparation and retention. I conduct both online and offline classes depending on the convenience of students. During my sessions, I use PPT presentations and whiteboard explanations to make learning more organized, visual, and engaging. My classes are interactive and focused on building confidence, helping students solve problems independently, and preparing them effectively for examinations. As a teacher, my aim is to help students develop a strong foundation in Chemistry and remove the fear many students have towards the subject. I believe that with the right guidance, regular practice, and conceptual understanding, every student can excel in Chemistry. Helping students improve academically and achieve success in their exams continues to motivate me in my teaching journey.
As per my son's experience, he clears all the concepts and teaches very well, explaining repeatedly until it is fully understood.
Top Tutor
Tezpur Airpur Area, Tezpur
7 yrs of
Exp
2 students
421 hrs of classes completed
450
per hour
Online Classes
Tutor's home
I am a mathematics teacher. I have been working in schools from last 6-7 years , and i was giving tutions at my home and even in an insitute in delhi from last 5-7 years. I shifted to tezpur,Assam in April 2021. my last job was in air force school hindan and I currently work at Air force school tezpur. i have a degree in msc mathematics and b.ed. i teach mathematics upto class 12. my key skills are in ms office , mathematics project, calligraphy , and can help out students in their various activities.
She is really amazing tutor you can ever have.She guides her students really well.She helps her students everytime. She motivates her students always. She supports her students always. She explains really nicely.
Top Tutor
Anna Nagar Mullai Nagar, Chennai
9 yrs of
Exp
10 students
416 hrs of classes completed
600
per hour
Online Classes
Student's Home
Hi, I'm Kalaiselvi, an M.Sc. Mathematics graduate with 9 years of experience in one-on-one online Maths tutoring. I specialize in teaching Classes 10, 11, and 12 for CBSE and Tamil Nadu State Board. My classes are conducted in both English and Tamil (bilingual), making concepts easy to understand. I focus on concept clarity, problem-solving, regular practice, and exam preparation, with personalized attention for every student.
Math class was interesting at times, especially when the topics were explained with real-life examples.The mix of learning and problem-solving made the experience enjoyable and not just about memorizing formulas.This made math feel more flexible and creative rather than just following one method.
Top Tutor
Banashankari, Bangalore
4 yrs of
Exp
5 students
271 hrs of classes completed
600
per hour
Online Classes
I am a commerce postgraduate from Pune University. Currently I am pursuing Ph.D in Commerce at one of the prestigious institutes for Commerce studies- Christ University, Bangalore. I have taught all the subjects of commerce to 11th & 12th Students since 4 years and BCom since 2 years. I have a good command on economics & accounts. I have a passion for teaching and have good understanding and practical exposure of these subjects. I also havd remotely worked as a Manager of Finance for a private firm in Maharashtra which makes me well versed in practical application of the subjects I teach.
Maam is very understanding. Explains concepts differently from school teaching making easy to learn and remember.
Top Tutor
Tollygunge, Kolkata
5 yrs of
Exp
3 students
38 hrs of classes completed
800
per hour
Online Classes
I have been giving tuitions to Class 12 students since October 2015. I was then in 2nd year of BSc Physics from the renowned 200 years old university, Presidency University. In total I taught 2 Class 12 students in Kolkata and 9 Class 12 students in Delhi. Currently I am teaching a Class 11 student from JNU Quarters Maths, Physics and Chemistry via Zoom app. I have whiteboard, colourful pens and other requirements to ease the teaching in a great way.
He has great ability to teach students by making intricate concept clear.he is also very honest.he gives full attention to me and never made me feel uncomfortable during the class.
