Question

One vertex of an equilateral triangle is $(2,3)$ and the equation of line opposite to the vertex is $x + y = 2$, then the equation of remaining two sides are

• A. $y-3=\left(2\pm\sqrt{3}\right)\left(x-2\right)$
• B. $y+3=\left(2\pm\sqrt{3}\right)\left(x+2\right)$
• C. $y+3=\left((3\pm\sqrt{2}\right)\left(x+2\right)$
• D. $y-3=\left(3\pm\sqrt{2}\right)\left(x-2\right)$

Answer 1

Answer: (A)

$y-3=\left(2\pm\sqrt{3}\right)\left(x-2\right)$

Answer 2

Since the two sides make an angle of $60^{?}$ each with side $x + y = 2$. Therefore equations of these sides will be $y-3=\frac{-1\pm tan^{?}\,60^{?}}{1\mp\left(-1\right)tan\,60^{?}}\left(x-2\right)=\frac{-1\pm\sqrt{3}}{1\pm\sqrt{3}}\left(x-2\right)$ $\Rightarrow y-3=\left(2\pm\sqrt{3}\right)\left(x-2\right)$