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Let A(0,6,6), B(6,6,0) and C(6,0,6) are ...

Let `A(0,6,6)`, B(6,6,0) and C(6,0,6) are three points and point D is moving on the line `x+z-3=0=y`. If G is centroid of `DeltaABC`, then minimum value of GD is

A

`sqrt((47)/2)`

B

`sqrt((37)/2)`

C

`sqrt((57)/2)`

D

`sqrt((23)/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
G=(4,4,4)
Let D=(a,0,3-a)
`GD^(2)=(a-4)^(2)+(0-4)^(2)+(3-a-4)^(2)`
`=2a^(2)-6a+33`.
For minimum of `GD^(2),a=3/2`
`GD_("min") = sqrt(2.9/4-6.3/2+33)=sqrt(57/2`
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