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AP EAMCET2011MathematicsStraight Lines

The line joining the points A(2,0) and B(3,1) is rotated through an angle of 45^ , about A in the anti-clockwise direction. The coordinates of B in the new position

Options

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

Correct answer

A. (2, 2 )

Step-by-step solution

Slope of A B= 1-0 3-2 =1 Therefore, B A X=45^ But B A C=45^ C A X=90^ So, the equation of A C is x-2 90^ = y-9 90^ =r (say) We have A B= (3-2)^2+(1-0)^2 = 2 As A C is the new position of A B , therefore A C=A B= 2 thus, the coordinates of C are given by x-2 90^ = y-0 90^ = 2 x=2, y= 2 Hence, the coordinates of C are (2, 2 ) .

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