The coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1,0) and (2,0) respectively. The equation of the diagonal CE is:

Options

A. `sqrt(3) x+y=4`
B. `x+sqrt(3)y +4 =0`
C. `x+sqrt(3)y =4`
D. none of these

Answer

C

Explanation

AB=1
`"or " C-=(2+1 xx "cos" 60^(@), 1 xx "sin" 60^(@)) -= ((5)/(2), (sqrt(3))/(2))`
`E-=(1,1 xx "sin" 60^(@)+1 xx "sin" 60^(@)) -=(1, sqrt(3))`
Therefore, the equation of CE is
`y-sqrt(3) = -(1)/(sqrt(3))(x-1)`