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Question

One vertex of the equilateral triangle with centriod at origin and one side as x+y2=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+y2=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+b2|2=3×22(a+b2)=6a+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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