    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 (2−22,2−02,2−22)=(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=2−0=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+4z−2=0→2x+y+2z−1=0  Suggest Corrections  0      Similar questions  Related Videos   Image of a Point with Respect to a Plane
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