Find the coordinates of one vertex of an equilateral triangle with centroid at the origin and the opposite side `x +y-2 =0`.

Explanation

let the coordinates of triangle be A,B,C respectively.

let D be the perpendicular from A to D having coordinates (h,k) and `(alpha, beta)` respectively

let the centroid be G having coordinates (0,0).

now, G= `((2*alpha+h)/3 , (2*beta+k)/3) `

`2*alpha + h=0` --- eqn(1)

`2*beta+k=0` ------ eqn(2)

`alpha+beta = 2` --- eqn (3)

now, `(k-0)/(h-0)*(-1) = -1`

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