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Exercise - 4.3

Question-1 :-  Find 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)determinant
  Hence area of triangle = 15/2  square unit
    
(ii)determinant
  Hence area of triangle = 47/2 square unit
    
(iii)determinant 
  Hence area of traingle = 15 square unit
    

Question-2 :-  Show that points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.

Solution :-
        determinant
    

Question-3 :-  Find values 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) determinant
    
(ii) determinant
    

Question-4 :-  (i) Find equation of line joining (1, 2) and (3, 6) using determinants.
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants.

Solution :-
(i) determinant
    
(ii) determinant
    

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 :-
 determinant
  The correct answer is D.
    
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