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in 3D Coordinate Geometry by (55.0k points)
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The image of the point P(1, 3, 4) in the plane 2x – y + z + 3 = 0, is 

A. (3, -5, 2) 

B. (3, 5, -2) 

C. (3, 5, 2) 

D. (-3, 5, 2)

1 Answer

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by (49.9k points)
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Best answer

Given: Equation of plane is 2x – y + z + 3 = 0. P is at (1, 3, 4) 

To find: image of P 

Explanation:

From the figure, P’ is the image of P and B is the midpoint of PP’ 

If B is (a, b, c), then

So any point on the line PB will be of the form 

x = 2λ +1, y = -λ + 3, z = λ + 4 

Since (a, b, c) will also be of this form we can substitute these values in (1) 

⇒ 2(2λ + 1) – (-λ + 3) + (λ + 4) + 3 = 0 

⇒ 4λ + 2 + λ – 3 + λ + 4 + 3 = 0 

⇒ 6λ = -6 

⇒ λ = -1 

So (a, b, c) = (-1, 4, 3) 

Substituting these values in the equations of a, b and c,

Therefore, 

x1 = -3, y1 = 5, z1 = 2 

 Therefore, the image is (-3, 5, 2)

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