Question

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

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

Answer 1

Answer: (B)

Any point P on the given line is $(2r+1,-3r-1,8r-10)$
So the direction ratios of AP are $2r,-3r-1,8r-10$.
Now AP is perpendicular to the given line if $2(2r)-3(-3r-1)+8(8r-10)$ = 0
$\Rightarrow$ $77r-77=0\Rightarrow r=1$
and thus the coordinates of P, the foot of the perpendicular from A on the line are $(3,-4,-2)$.
Let B $(a,b,c)$ be the reflection of A in the given line. Then P is the mid-point of AB
$\frac{a+1}{2}=3,\frac{b}{2}=-4,\frac{c}{2}=-2$
$\Rightarrow$ $a$ = 5, $b$ = 8, $c$ = - 4
Thus the coordinates of required point are (5, -8, -4).