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Find the image of the point (1, 0,0) wit...

Find the image of the point (1, 0,0) with respect to the line `(x-1)/(2)= (y+1)/(-3)= (z+ 10)/(8)`

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.
`therefore 2t xx 2 + (1 + 3t)3 + (-10 + 8t) 8 = 0`
77t - 77 = 0 `rArr` 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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