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  4. 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

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Q. 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

JEE MainJEE Main 2023Straight Lines

Solution:

image
At $A x=y$
$Y-2 x=2$
$(-2,-2)$
Height from line $x + y =0$
$h=\frac{4}{\sqrt{2}}$
Area of $\Delta=\frac{\sqrt{3}}{4} \frac{ h ^2}{\sin ^2 60}=\frac{8}{\sqrt{3}}$