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KVPY2017MathematicsStraight Lines

Let A = ( a ₁, a ₂ ) and B = ( b ₁, ~b ₂ ) be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between A and B ?

Options

  1. A65
  2. B74
  3. C83
  4. D97

Correct answer

C. 83

Step-by-step solution

AB = ( a ₁- b ₁ )²+ ( a ₂- b ₂ )² Square + Square = 65 possible when =64+1 array l 74 =49+25 97 =81+16 array But 83 not possible

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