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AP EAMCET20227 Jul 2022Evening ShiftMathematicsStraight LinesActual

Suppose A B O C is a rhombus in the first quadrant with O being the origin. If the vertices B and C of A B C lie respectively on y= 4 3 x and y=0 and the side B C passes through ( 2 3 , 2 3 ) , then the mid-point of B C is

Options

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

Correct answer

A. ( 4 5 , 2 5 )

Step-by-step solution

aligned & 2 = 4 3 , =x & 2 x 1-x^2 = 4 3 2 x^2+3 x-2=0 aligned x= 1 2 or -2 As is acute, x= 1 2 = Slope of B C=-2 [as B C O A ] Equation of B C=2 x+y=2 [ as ( 2 3 , 2 3 ) lies on B C ] B ( 3 5 , 4 5 ) and C (1,0) Mid-point of B C ( 4 5 , 2 5 )

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