NCERT Solutions for Maths Class 12 Exercise 4.3
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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.
NCERT Solutions for Maths Class 12 Exercise 4.3 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.
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NCERT Solutions for Maths Class 12 Exercise 4.3 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.
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NCERT Solutions for Maths Class 12 Exercise 4.1
NCERT Solutions for Maths Class 12 Exercise 4.2
NCERT Solutions for Maths Class 12 Exercise 4.4
NCERT Solutions for Maths Class 12 Exercise 4.5
NCERT Solutions for Maths Class 12 Exercise 4.6
NCERT Solutions for Maths Class 12 Exercise 4.3
Maths Class 12 Ex 4.3 Question 1.
Find the area of the triangle with vertices at the point given in each of the following:(i) (1, 0), (6, 0), (4, 3)
(ii) (2, 7), (1, 1), (10, 8)
(iii) (–2, –3), (3, 2), (–1, –8)
Solution:
(i) Area of a triangle = 
= 1/2 [1(0 – 3) + 1(18 – 0)]
= 1/2 [1 × (–3) + 1 × 18]
= 1/2 [–3 + 18]
= 1/2 [15]
= 7.5 sq. units
Maths Class 12 Ex 4.3 Question 2.
Show that the
points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.
Solution:
Let us assume that the vertices of ∆ABC are A (a, b + c), B (b, c + a) and C
(c, a + b).
Maths Class 12 Ex 4.3 Question 3.
Find the value of k if area of triangle is 4 sq. units and vertices are(i) (k, 0), (4, 0), (0, 2)
(ii) (–2, 0), (0, 4), (0, k)
Solution:
(i) Area of a triangle = 4 sq. units
(given)
Area of the triangle = 
= 1/2 [–2k + 8]
= –k + 4
Case (a): –k + 4 = 4 ⇒ k = 0
Case (b): –k + 4 = –4 ⇒
k = 8
Hence, k = 0, 8
(ii) The area of the triangle whose
vertices are (–2, 0), (0, 4),
(0, k).
Maths Class 12 Ex 4.3 Question 4.
(i) Find the
equation of line joining (1, 2) and (3, 6) using determinants.
(ii) Find the equation of line joining (3, 1) and (9, 3) using determinants.
Solution:
(i) The given points are (1, 2) and
(3, 6)
Equation of the line is
Maths Class 12 Ex 4.3 Question 5.
If area of triangle is 35 sq. units with vertices (2, –6), (5, 4) and (k, 4), then k is(A) 12
(B) –2
(C) –12, –2
(D) 12, –2
Solution:
It is given that the area of the triangle is 35 sq. units.
Area of a triangle
= 
= 1/2 [50 – 10k] = 25 – 5k
∴ 25 – 5k = 35 or 25 – 5k = –35
–5k = 10 or 5k = 60
⇒ k = –2 or k = 12
Hence, option (D) is correct.
NCERT Solutions for Maths Class 12 Exercise 4.1
NCERT Solutions for Maths Class 12 Exercise 4.2
NCERT Solutions for Maths Class 12 Exercise 4.4