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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

If one vertex of a equilateral triangle of side 2 lies at the origin and other lies on the line x- 3 y=0 , then the coordinates of the third vertex are

Options

  1. A(0,2)
  2. B(- 2 , 2 )
  3. C(2,0)
  4. D(- 3 , 1)

Correct answer

D. (- 3 , 1)

Step-by-step solution

The equation of line x- 3 y=0 in parametric form is x-0 30^ = y-0 30^ =r x-0 3 2 = y-0 1 2 =r Put r= 2 , we get ( 3 , 1) and (- 3 ,-1) Case-1 : Consider two vertices of an equilateral triangle of side 2 as (0,0) and ( 3 , 1) . Equation of line which is perpendicular bisector of (0,0) and ( 3 , 1) is gathered x - 3 2 120^ = y - 1 2 120^ =r₁ (let) Put r₁= 3 ( As altitude = 3 ) gathered x= 3 2 3 (- 1 2 ) ; y= 1 2 3 ( 3 2 ) x= 3 2 3 2 ; y= 1 2 3 2 Third vertex can be (0,2) and ( 3 ,-1) Case-2 : Consider two vertices of

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