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  • The reflection of the point (α, β, γ) in the xy- plane is: A. (α, β, 0) B. (0, 0, γ) C. (-α, -β, -γ) D. (α, β, -γ)

 Q: The reflection of the point (α, β, γ) in the xy- plane is:
A. (α, β, 0)
B. (0, 0, γ)
C. (-α, -β, -γ)
D. (α, β, -γ)

 

Answers (1)

The equation of the XY plane is Z = 0

Given point (α, β, γ); if we draw a perpendicular from this point in the  XY plane, the coordinates of the plane will be

(α, β, 0).

Let the reflection be (x, y, z)

So, \alpha=\frac{\alpha+x}{2}

=> x = α

\beta=\frac{\beta+y}{2}

=> y = β

0=\frac{\gamma+z}{2}

=> z = -γ

The reflection is: (α, β, -γ). (option D)

 

Posted by

infoexpert24

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