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

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 (A) 2 √3 (B) (8/√3) (C) 3 √3 (D) (10/√3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5e6e94c5b8f79ee2dba6b6fbc83d63fd-.png" /> At A x=y Y-2 x=2 (-2,-2) Height from line x + y =0 h=(4/√2) Area of Δ=(√3/4) ( h 2/ sin 2 60)=(8/√3)

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 $△ A BC$ is an equilateral triangle. Then, the area of the $△ A BC$ is

$23$

$\frac{8}{3}$

$33$

$\frac{10}{3}$

At $A x = y$
$Y - 2 x = 2$
$(- 2, - 2)$
Height from line $x + y = 0$
$h = \frac{4}{2}$
Area of $Δ = \frac{3}{4} \frac{h ^{2}}{s i n ^{2} 60} = \frac{8}{3}$

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−2x=2 such that △ABC is an equilateral triangle. Then, the area of the △ABC is

23​

3​8​

33​

3​10​