question_answer

If the three points (0, 1),\[(0,-1)\]and\[(x,0)\]are vertices of an equilateral triangle, then the values of\[x\]are

A)  \[\sqrt{3},\sqrt{2}\]

B)                         \[\sqrt{3},-\sqrt{3}\]

C)  \[-\sqrt{5},\sqrt{3}\]    

D)         \[\sqrt{2},-\sqrt{2}\]

E)  \[\sqrt{5},-\sqrt{5}\]

Correct Answer: B

Solution :

Since, triangle is equilater. \[\therefore \]  \[\angle ACB=60{}^\circ \] \[\therefore \]  \[\angle ACD=30{}^\circ \] Now, in right angle triangle\[\Delta ADC,\] \[\tan 30{}^\circ =\frac{1}{x}\] \[\Rightarrow \]               \[\frac{1}{\sqrt{3}}=-\frac{1}{x}\] \[\Rightarrow \]               \[x=-\sqrt{3}\] Similarly, in right angle triangle BDC                 \[\tan 30=-\frac{1}{x}\] \[\Rightarrow \]               \[\frac{1}{\sqrt{3}}=-\frac{1}{x}\] \[\Rightarrow \]               \[x=-\sqrt{3}\]