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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

In the equilateral triangle A B C , the equation of the side B C is x + y - 2 = 0 and the centroid of ∆ A B C is 0 , 0 . If the points A , B , C are in anticlockwise order, then the midpoint of the line segment joining A and C is

Options

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

Correct answer

B. - 3 - 1 2 , 3 - 1 2

Step-by-step solution

Foot of 0,0 on B C is D 1,1 ⇒ O D = 2 ⇒ Slope of O D is 1 ⇒ O E makes an angle 45 o + 120 o = 165 o with the positive x -axis ⇒ E = 2 cos ⁡ 165 o , 2 sin ⁡ 165 o = - 3 - 1 2 , 3 - 1 2

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