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Manipal MET2019MathematicsStraight Lines

The base of vertices of an isosceles triangle P Q R are Q(1,3) and R(-2,7) . The vertex P can be

Options

  1. A(1,6)
  2. B( 1 2 , 5 )
  3. C( 5 6 , 6 )
  4. DNone of these

Correct answer

C. ( 5 6 , 6 )

Step-by-step solution

Given that, the base of an isosceles triangle P Q R are Q(1,3) and R(-2,7) . Let the co-ordinates of point P are (x, y) . In an isosceles triangle P Q=P R array cc i.e. & (x-1)^2+(y-3)^2 & = (x+2)^2+(y-7)^2 & (x-1)^2+(y-3)^2=(x+2)^2+(y-7)^2 & x^2-2 x+1+y^2-6 y+9 & =x^2+4 x+4+y^2-14 y+49 & -2 x-6 y+10=4 x-14 y+49+4 & -6 x+8 y=43 array Here, option ' 3 ' (5 / 6,6) satisfies the equation. Co-ordinate of P are (5 / 6,6) .

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