First slide

Introduction to 3-D Geometry

Question

$α, β, γ are the root of x^{3} - 2 x^{2} - x + 2 = 0 . Centroid of triangle with verties α, β, γ, (β, γ, α), (γ, α, β)$

Moderate

A

$(- \frac{2}{3}, \frac{2}{3}, - \frac{2}{3})$
B

$(- \frac{2}{3}, \frac{1}{3}, \frac{2}{3})$
C

$(\frac{2}{3}, \frac{2}{3}, \frac{2}{3})$
D

$(\frac{4}{3}, \frac{2}{3}, \frac{2}{3})$

Solution

$α, β, γ are the root of x^{3} - 2 x^{2} - x + 2 = 0 \Rightarrow α + β + γ = 2 ∴ c e n t r o i d G = (\frac{α + β + γ}{3}, \frac{β + γ + α}{3}, \frac{γ + α + β}{3}) = (\frac{2}{3}, \frac{2}{3}, \frac{2}{3})$

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