MathematicsThe area of a triangle with vertices (a,b+c)  , (b,c+a)   and (c,a+b)   is

The area of a triangle with vertices (a,b+c)  , (b,c+a)   and (c,a+b)   is


  1. A
    2 sq unit
  2. B
    0
  3. C
    1 sq unit
  4. D
    3 sq unit 

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    Solution:

    It is given that the vertices of the triangle are A a,b+c B b,c+a ,C c,a+b  .
    We know that, area of a triangle is given by Area= 1 2 x 1 y 2 y 3 + x 2 y 3 y 1 + x 3 y 1 y 2  .
    Here,
    x 1 =a, x 2 =b, x 3 =c, y 1 =b+c, y 2 =c+a,and y 3 =a+b  .
    Then,
    Therefore, the area of the triangle is 0 only.
    Hence, option (2) is correct.
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