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Manipal MET2021MathematicsStraight Lines

The point on the line y=x equidistant from (4,0) and (5,1) is

Options

  1. A(2,2)
  2. B(3,3)
  3. C( 5 2 , 5 2 )
  4. D( 1 2 , 1 2 )

Correct answer

C. ( 5 2 , 5 2 )

Step-by-step solution

Let the required point is (a, a) . (4-a)^2+a^2=(5-a)^2+(1-a)^2 array ll & 16+a^2-8 a+a^2= 25+a^2 -10 a+1+a^2-2a & 16-25-1+a^2+a^2-a^2-a^2-8 a+10 a+2 a=0 & 4 a=10 & a= 10 4 = 5 2 array Required point is ( 5 2 , 5 2 ) .

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