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AP EAMCET20228 Jul 2022Evening ShiftMathematicsFunctionsActual

For x and y satisfying |x|+|y|=|x-3|+|y-2| , which of the following is correct?

Options

  1. Ax= 1 2 for 0 x < 3 and 1 y < 2
  2. Bx+y= 5 2 for x 3 and y 2
  3. Cx= 1 2 for x 2 and 0 y < 3
  4. Dx+y= 5 2 for 0 x < 3,0 y < 2

Correct answer

D. x+y= 5 2 for 0 x < 3,0 y < 2

Step-by-step solution

|x|+|y|=|x-3|+|y-2| Case I 0 x < 3 and 0 y < 2|x|+|y|=|x-3|+|y-2| x+y=-(x-3)-(y-2) aligned & x+y=-x+3-y+2 & 2 x+2 y=5 x+y=5 / 2 aligned Case II x 3 and y 2|x|+|y|=|x-3|+|y-2| x+y=x-3+y-2 x=-5 which is wrong. Option (d) is true.

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