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The image of the point A (1,0,0) in the ...

The image of the point A (1,0,0) in the line `(x - 1)/(2) = (x + 1)/(-3) = (z + 10)/(8)` is :

A

`(5,-8,-4)`

B

`(3,-4,2)`

C

`(5,-4,-8)`

D

`(3,4,-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
A point on the line ` (x-1)/(2) = (y+1)/(-3) = (z + 10)/(8) = t ` is
` P(1 + 2t , -1 -3t , -10+ 8t)`
The d.r. s of AP are 2t , -1-3t, -10 + 8t
The line AP is perpendicular to the line with d.r.s 2,-3,8.
`:. 2t xx 2 + (1 +3t)3 + (-10 + 8t) 8 =0`
` 77t - 77 =0 implies t =1 `
(i) gives p (3,-4,-2) Which is foot of perpendicular .
By midpoint rule , the image of A (1,0,0) is (5,-8,-4) .
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