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KVPY2015MathematicsStraight Lines

Let ABCD be a square of a side length 1 , Let P , Q , R , S be points in the interiors of the sides A D, B C, A B, C D , respectively, such that P Q and RS intersect at right angles. If P Q= 3 3 4 then RS equals

Options

  1. A2 3
  2. B3 3 4
  3. C2 +1 2
  4. D4-2 2

Correct answer

B. 3 3 4

Step-by-step solution

PQ RS c-a=b-d array l P Q= 3 3 4 P Q²= 27 16 1+(a-c)²= 27 16 R S= (b-d)²+1 array By equation (1),(2) and (3) R S= 3 3 4

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