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

The image of the point `(-1, 3, 4)` in the plane `x-2y=0` is

A

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

B

(15,11,4)

C

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

D

`(9/5,(-13)/(5),4)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of line PQ is `(x+1)/(1)=(y-3)/(-2)=(z-4)/(0)=lambda`

For some suitable value of `lambda,` coordinates of point `Q(lambda -1, 3 - 2lambda, 4) ` R is the midpoint of P and Q `therefore R=((lambda-2)/(2),(6-2lambda)/(2),4), therefore R-=(lambda/2-1,3 lambda,4)`
It satisfies `x-2y=0 rArr lambda=14/5`
`Q=(9/5,-13/5,4)`
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