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AP EAMCET202017 Sep 2020Evening ShiftMathematicsStraight LinesActual

The image of the point (P(3,8) ) with respect to the line (x+3 y=7 ), assuming the line to be a plane mirror, is equal to .........

Options

  1. A((1,4) )
  2. B((-1,4) )
  3. C((1,-4) )
  4. D((-1,-4) )

Correct answer

D. ((-1,-4) )

Step-by-step solution

Let image is (P^ (h, k) ) Then (P P^ ) is perpendicular to given line and mid point of (P P^ ) lies over line. So, we have ( aligned & & ( 8-k 3-h ) -1 3 & =-1 & & 8-k & =3(3-h) (i) & And, & 3+h 2 +3 ( 8+k 2 ) & =7 & & 3+h+24+3 k & =14 (ii) & & h+3 k+13 & =0 aligned ) ( ) (h=-1 and k=-4 ) So image is, ((-1,-4) ).

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