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KCET2023MathematicsStraight Lines

The area of a triangle with vertices (-3,0) , (3,0) and (0, k) is 9 sq units, find the value of k is

Options

  1. A-9
  2. B6
  3. C3
  4. D9

Correct answer

C. 3

Step-by-step solution

We know that areas of a triangle with vertices (x₁, y₁ ), (x₂, y₂ ) and (x₃, y₃ ) is given by aligned & = 1 2 | array lll x₁ & y₁ & 1 x₂ & y₂ & 1 x₃ & y₃ & 1 array | & = 1 2 | array ccc -3 & 0 & 1 3 & 0 & 1 0 & k & 1 array | aligned Expanding along C₂9= 1 2 [-k(-3-3)] 18=3 k+3 k=6 k k= 18 6 =3

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