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Question

# One vertex of the equilateral triangle with centriod at origin and one side as x+y−2=0 is

A
(2,2)
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B
(2,2)
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C
(2,2)
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D
(2,2)
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Solution

## The correct option is A (−2,−2)Let the vertices of the triangle is A,B,C and D be the mid point of BC and BC lies in the line x+y−2=0 ∴A will lie in 3rd quadrant. ∵ the triangle is equilateral the centroid G(0,0) is also orthocenter and median AD is also its altitude and G divides it in the ratio 2:1. Let the coordinates of A be (a,b), then |a+b−2|√2=3×2√2⇒−(a+b−2)=6⇒a+b+4=0 ⋯(i) Equation of the line perpendicular to BC and passing through origin is x=y and A lie on it. ∴a=b Hence, coordinates of A is (−2,−2).

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