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JEE Main201815 Apr 2018Evening ShiftMathematicsStraight LinesActual

The sides of a rhombus A B C D are parallel to the lines, x-y+2=0 and 7 x-y+3=0 . If the diagonals of the rhombus intersect at P(1,2) and the vertex A (different from the origin) is on the y axis, then the ordinate of A is

Options

  1. A2
  2. B7 4
  3. C7 2
  4. D5 2

Correct answer

D. 5 2

Step-by-step solution

Let the coordinate A be (0, c) Equations of the given lines are x-y+2=0 and 7 x-y+3=0 We know that the diagonals of the rhombus will be parallel to the angle bisectors of the two given lines; y=x+2 and y=7 x+3 equation of angle bisectors is given as: aligned & x-y+2 2 = 7 x-y+3 5 2 &5 x-5 y+10= (7 x-y+3) aligned Parallel equations of the diagonals are 2 x+4 y-7=0 and 12 x-6 y+13=0 slopes of diagonals are -1 2 and 2 . Now, slope of the diagonal from A(0, c ) and passing through P(1,2) is (2-c) 2-c=2 c=0 (not possibl

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