Question

If the three points $(0,1),(0,-1)$ and $(x,0)$ are vertices of an equilateral triangle, then the value of x are :

• A. $\sqrt{3},\sqrt{2}$
• B. $\sqrt{3},-\sqrt{3}$
• C. $-\sqrt{5},\sqrt{3}$
• D. $\sqrt{2},-\sqrt{2}$

Answer 1

Answer: (B)

$\sqrt{3},-\sqrt{3}$

Since, $A(0,1),B(0,-1)$ and $C(x,0)$ are the vertices of an equilateral $△ABC$
$\therefore AB=BC=CA$
$\Rightarrow \sqrt{0+4}=\sqrt{x^2+1}$
$\Rightarrow x^2=3$
$\Rightarrow x=\pm \sqrt{3}$