Question

The reflection of the point P(1,0, 0) in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{x+10}{8}$ is

• A. (3, -4, -2)
• B. (5, - 8, - 4)
• C. (1, - 1, - 10)
• D. (2, - 3, - 8)

Answer 1

The correct option is B (5, - 8, - 4)

Coordinates of any point Q on the given line are
(2r +1, - 3r - 1, 8r - 10).
So the direction cosines of PQ are 2r, - 3r - 1, 8r - 10.
Now PQ is perpendicular to the given line.
If 2(2r) -3 (-3r-1) + 8 (8r- 10) = 0
$\Rightarrow$ 77r - 77 = 0 $\Rightarrow$ r = 1
And the coordinates of Q, the foot of the perpendicular from P on the line are (3, - 4, - 2).
Let R (a, b, c) be the reflection of P in the given lines than Q is the mid- point of PR
$\Rightarrow \frac{a+1}{2}=3,\frac{b}{2}=-4,\frac{c}{2}=-2$
$\Rightarrow a=5,b=-8,c=-4$
And the coordinate of the required point are (5, - 8, - 4).