Q. 355.0( 1 Vote )

Mark against the A. (3, -5, 2)

B. (3, 5, -2)

C. (3, 5, 2)

D. (-3, 5, 2)

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





B lies on the plane.


So, 2a – b + c + 3 = 0 … (1)


Also, equation of line PB is



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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