Question

The image of the point $A(1,2,3)$ relative to the plane $\pi$ is $B(3,6,-1)$. The equation of the plane $\pi$ is

• A. $x+2y+3z-1=0$
• B. $x+2y-2z+8=0$
• C. $x-2y+2z-8=0$
• D. $x+2y-2z-8=0$

Answer 1

The correct option is D $x+2y-2z-8=0$

Midpoint of segment $AB$ is $(\frac{1+3}{2},\frac{2+6}{2},\frac{3-1}{2})\equiv (2,4,1)$
Direction ratios of segment (normal) $AB$ are $(2,4,-4)$
Hence, equation of the plane $\pi$ is given by
$2(x-2)+4(y-4)-4(z-1)=0$
$\Rightarrow 2x+4y-4x-16=0$
$\Rightarrow x+2y-2z-8=0$