Question

The reflection of the point $A(1,0,0)$ in the line $\frac{x-1}{2}=\frac{y+2}{-3}=20-$ z is

• A. $(3,-4,-2)$
• B. $(5,-10,38)$
• C. $(1,-1,-10)$
• D. $(2,-3,8)$

Answer 1

The correct option is B $(5,-10,38)$

The cartesian equation of the line is $\frac{x-1}{2}=\frac{y+2}{-3}=\frac{20-z}{1}$ ----(1)

The given point is $(1,0,0)$

To find the image of $P(1,0,0)$ in the line draw a line PR ⊥ to the line .

Let R be the image of P and Q is the midpoint of PR

$a\times 2+b\times (-3)+c\times 1=0$ ......(2)

$2a-3b+c=0$

$\frac{x-1}{a}=\frac{y+0}{b}=\frac{0-z}{c}$

Any point on the line (2) is $(ak+1,bk+0,ck+0)$

Let the point be Q

But Q also lies online (1)

$\frac{ak+1-1}{2}=\frac{bk+2+2}{-3}=\frac{20+0-ck}{1}$

$\frac{ak0}{2}=\frac{bk+4}{-3}=\frac{20-ck}{1}$

$\frac{8+(a+4b-20c)k}{8}=1$

Hence the answer will be $(5,-10,38)$