Question

The image of the point $P(1,3,4)$ in the plane $2x-y+z+3=0$, is

• A. $(3,5,-2)$
• B. $(-3,5,2)$
• C. $(3,-5,2)$
• D. $(3,5,2)$

Answer 1

Answer: (B)

$(-3,5,2)$

Image of a point in a plane is

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}=\frac{-2(a{x}_1+b{x}_1+c{x}_1+d)}{a^2+b^2+c^2}\frac{x-1}{2}=\frac{y-3}{-1}=\frac{z-4}{1}=\frac{-2\left(2\right(1)-1(3)+1(4)+3)}{2^2+1^2+1^2}\frac{x-1}{2}=\frac{y-3}{-1}=\frac{z-4}{1}=-2\Rightarrow x=-3,y=5,z=2$

So, the image of $P$ in the given plane is $(-3,5,2)$.

So, option B is correct.