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Highly selective Backlog Qs for JEE MainMathematicsStraight Lines

A rectangle (A B C D ) has its side parallel to the line (y=2 x ) and vertices (A, B, D ) are on lines (y=1, x=1 ) and (x=-1 ) respectively. The coordinate of (C ) can be

Options

  1. A((3,8) )
  2. B((-3,8) )
  3. C((-3,-1) )
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Hint: Case I line (y=2 x (1) ) (A D ) parallel to (y=2 x ) ( M _ AD =2 ~ &~ M _ AB =- 1 2 ) for (a=3 ) (A(3,1), B(1,2), C(-3,-6), D(-1,-7) ) ( aligned & for a=-3 & C(3,3), A(-3,1), B(1,-1), D(-1,5) aligned ) Case II AD perpendicular to line (1) ( M_ A D = 1 2 , M_ A B =2 b=3-2 a d= a+1 2 ) for (a=3, C(-3,-2) ) for (a=-3, C(3,7) ) ( ^* ) In both cases if abscissa of (C: 3 ) or -3 then co-ordinates of (C ) can be ((3,3) ) or ((3,7) ) or ((-3,-6) ) or ((-3,-2) )

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