Let B and C be the two points on the line y+x=0 such that B and C are symmetric with respe…

Question

Let $B$ and $C$ be the two points on the line $y+x=0$ such that $B$ and $C$ are symmetric with respect to the origin. Suppose $A$ is a point on $y-2 x=2$ such that $$\triangle A B C$$ is an equilateral triangle. Then, the area of the $$\triangle A B C$$ is :

Accepted Answer

Origin $(O)$ is mid-point of $B C(x+y=0)$.

$A$ lies on perpendicular bisector of $B C$, which is $x-y=0$

A is point of intersection of $x-y=0$ and $y-2 x=2$

$\therefore A \equiv(-2,-2)$

Let $h=A O=\frac{-2-2}{\sqrt{1^{2}+1^{2}}}=2 \sqrt{2}$

$$
\text { Area }=\frac{h^{2}}{\sqrt{3}}=\frac{8}{\sqrt{3}}
$$

Solutions · 1