Question

Find the equation of the plane for which the mirror of (2,2,2) is (-2,0,-2)

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

Answer 1

Answer: (C)

2x+y+2z-1=0

Since the mirror of the (2,2,2) is (-2,0,-2), then the midpoint of the line joining these points is on the plane.
So the coordinates of the midpoint are

$\left(\frac{2-2}{2},\frac{2-0}{2},\frac{2-2}{2}\right)=\left(0,1,0\right)$
The line joining these points is perpendicular to the plane.
So,the direction ratios of the plane are
$a=2-(-2)=4b=2-0=2c=2-(-2)=4$
The equation of the plane is
$\mathrm{ax}+\mathrm{by}+\mathrm{cz}+d=0\mathrm{putting}\mathrm{the}\mathrm{values}\mathrm{of}\mathrm{the}a,b,c\mathrm{in}\mathrm{the}\mathrm{above}\mathrm{equation},\mathrm{we}\mathrm{get}4x+2y+4z+d=0\dots \left(1\right)\mathrm{Now}\mathrm{put}\mathrm{the}\mathrm{coordinate}s\mathrm{of}\mathrm{the}\mathrm{midpoint},\mathrm{we}\mathrm{get}2+d=0d=-2.\mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}d\mathrm{in}\left(1\right)\mathrm{The}\mathrm{equation}\mathrm{of}\mathrm{plane}\mathrm{is}4x+2y+4z-2=0\to 2x+y+2z-1=0$