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AP EAMCET2011MathematicsStraight Lines

The image of the point (3,8) in the line x+3 y=7 is

Options

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

Correct answer

C. (-1,-4)

Step-by-step solution

The equation of perpendicular line on x+3 y=7 is 3 x-y+ =0 . Since, it is passes through (3,8) . aligned & 9-8+ =0 & =-1 & 3 x-y-1=0 & aligned The point of intersection of lines x+3 y=7 and 3 x-y-1=0 is (1,2) , which is the foot of a point. Let the image of a point (3,8) be (x₁, y₁ ) . array ll & 3+x₁ 2 =1, 8+y₁ 2 =2 & x₁=-1, y₁=-4 array

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