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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Let A B C is an equilateral triangle. If the coordinates of the base are B(1,-1) and C(5,2) , then the coordinates of vertex A can be

Options

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

Correct answer

D. (3- 3 3 2 , 1 2 +2 3 )

Step-by-step solution

We have B C= (5-1)^2+(2+1)^2 = 16+9 =5 Also m_ B C = 2-(-1) 5-1 = 3 4 Midpoint of BC is M (3, 1 2 ) Now, equation of AM (in parametric form) is x-3 - 3 5 = y- 1 2 4 5 =r (r= 5 3 2 ) We get x =3 3 3 2 , y = 1 2 2 3

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