Question

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

• A. $x+\sqrt{3}y+4=0$
• B. $x+\sqrt{3}y=4$
• C. $\sqrt{3}x+y=4$
• D. $\sqrt{3}x+y+4=0$

Answer 1

The correct option is B $x+\sqrt{3}y=4$

$C=(2+1.\cos {60}^0,1.\sin {60}^0)=(\frac{5}{2},\frac{\sqrt{3}}{2})$

$E=(1,1-\sin {60}^0+1-\sin {60}^0)=(1,\sqrt{3})$

The equation of $CE$ is

$y-\sqrt{3}=\frac{\sqrt{3}-\frac{\sqrt{3}}{2}}{1-\frac{5}{2}}(x-1)\Rightarrow x+\sqrt{3}y=4$