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the image of the point (-1,3,4) in the p...

the image of the point `(-1,3,4)` in the plane `x-2y=0` a.`(-(17)/(3),(19)/(3),4)` b.(15,11,4) c.`(-(17)/(3),(19)/(3),1)` d.`((9)/(5),-(13)/(5),4)`

A

`(-17/3,-19/3,4)`

B

`(15,11,4)`

C

`(-17/3,-19/3,1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
The image `(alpha,beta,gamma)` of `(-1,3,4)` in the plane `x-2y+0z=0` is given by
`(alpha+1)/1=(beta-3)/(-2)=(gamma-4)/0=(-2(-1-6+0))/(1+4+0)`
`implies(alpha+1)/1=(beta-3)/(-2)=(gamma-4)/0=14/5impliesalpha=9/4,beta=(-13)/5,gamma=4`
Hence, he image is `(6/5,-13/5,4)`.
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