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=0Since 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 (2âˆ’22,2âˆ’02,2âˆ’22)=(0,1,0) The line joining these points is perpendicular to the plane. So,the direction ratios of the plane are a=2âˆ’(âˆ’2)=4b=2âˆ’0=2c=2âˆ’(âˆ’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=0â€¦(1)Now put the coordinates ofthe midpoint, we get 2+d=0d=âˆ’2.Put the value of d in (1)The equation of plane is4x+2y+4zâˆ’2=0â†’2x+y+2zâˆ’1=0

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