Let A(x1, y1), B(x2, y2) and C(x3, y3) be vertices of an equilateral triangle whose side is 4 units. Let Δ=| x1 y1 1 x2 y2 1 x3 y3 1 | then Δ2 is equal to

Question

Let A(x1, y1), B(x2, y2) and C(x3, y3) be vertices of an equilateral triangle whose side is 4 units. Let Δ=| x1 y1 1 x2 y2 1 x3 y3 1 | then Δ2 is equal to (A) 64 (B) 128 (C) 192 (D) 256

Tardigrade Admin · Accepted Answer

(1/2)|Δ|= text area of triangle =(√3/4)(4)2=4 √3 ⇒|Δ|=8 √3 ⇒ Δ2=192

Q. Let $A (x_{1}, y_{1}), B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$ be vertices of an equilateral triangle whose side is 4 units. Let $Δ = ∣ ∣ x_{1} x_{2} x_{3} y_{1} y_{2} y_{3} 111 ∣ ∣$ then $Δ^{2}$ is equal to

64

128

192

256

$\frac{1}{2} ∣Δ∣ = area of triangle = \frac{3}{4} (4)^{2} = 43$
$\Rightarrow ∣Δ∣ = 83 \Rightarrow Δ^{2} = 192$

Q. Let A(x1​,y1​),B(x2​,y2​) and C(x3​,y3​) be vertices of an equilateral triangle whose side is 4 units. Let Δ=∣∣​x1​x2​x3​​y1​y2​y3​​111​∣∣​ then Δ2 is equal to

64

128

192

256

21​∣Δ∣= area of triangle =43​​(4)2=43​ ⇒∣Δ∣=83​⇒Δ2=192

Q. Let $A (x_{1}, y_{1}), B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$ be vertices of an equilateral triangle whose side is 4 units. Let $Δ = ∣ ∣ x_{1} x_{2} x_{3} y_{1} y_{2} y_{3} 111 ∣ ∣$ then $Δ^{2}$ is equal to

$\frac{1}{2} ∣Δ∣ = area of triangle = \frac{3}{4} (4)^{2} = 43$
$\Rightarrow ∣Δ∣ = 83 \Rightarrow Δ^{2} = 192$