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AP EAMCET201922 Apr 2019Morning ShiftMathematicsStraight LinesActual

If the mid-points of the sides (B C, C A ) and (A B ) of a triangle (A B C ), are respectively ((2,1) ), ((-1,-2) ) and ((3,3) ), then the equation of the side (B C ) is

Options

  1. A(x-2 y=0 )
  2. B(5 x-4 y=6 )
  3. C(2 x+3 y=8 )
  4. D(3 x-2 y=6 )

Correct answer

B. (5 x-4 y=6 )

Step-by-step solution

Let the coordinate of (B ) is ((a, b) ). Mid-point of (B Q= ) Mid-point of (P R ) ( aligned & ( a-1 2 , b-2 2 )= ( 3+2 2 , 3+1 2 ) & a-1 2 = 5 2 & and b-2 2 = 4 2 & a=5+1 & and b=4+2 & a=6 and b=6 aligned ) ( B(6,6) ) and (P(2,1) ) Now, equation of (B C ) is ( array rlrl & y-6= 1-6 2-6 (x-6) & y-6= -5 -4 (x-6) & 4 y-24=5 x-30 & 5 x-4 y-30+24=0 & 5 x-4 y=6 array )

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