The equation of the side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the…
The equation of the side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is
$\frac{\sqrt{2}}{\sqrt{3}}$
$\frac{1}{2 \sqrt{3}}$
$\frac{\sqrt{3}}{\sqrt{2}}$
$\frac{2}{\sqrt{3}}$
Solution
Given : $x+y=2$ is equation of a side and $(2,-1)$ is vertex. Since $(2,-1)$ doesn't satisfy $x+y=2$
$\therefore \mathrm{It}$ is vertex opposite to the side.
Perpendicular distance from $(2,-1)$ to $x+y=2$ is height of the triangle $=\frac{1-11}{\sqrt{2}}=\frac{\sqrt{3}}{2} \times$ Side $\Rightarrow$ Side $=\sqrt{\frac{2}{3}}$.