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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
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B
-2x-2z=0
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C
2x+y+2z-1=0
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D
2x+3y+2z=3
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Solution

The correct option is D 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

(222,202,222)=(0,1,0)
The line joining these points is perpendicular to the plane.
So,the direction ratios of the plane are
a=2(2)=4b=20=2c=2(2)=4
The equation of the plane is
ax+by+cz+d=0putting the values of the a,b,cin the above equation, we get4x+2y+4z+d=0(1)Now put the coordinates ofthe midpoint, we get 2+d=0d=2.Put the value of d in (1)The equation of plane is4x+2y+4z2=02x+y+2z1=0

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