Question

The image of the point P(3, 5, 7) in the plane 2x + y + z = 0 is 

(A) (9, 1, −1) 

(B) (−9, −1, 1) 

(C) (−9, 1, −1) 

(D) (9, −1, −1)

Answer 1

Correct option is (B) -9,-1,1

Explanation :

See Fig. Let Q(x₁, y₁, z₁) be the foot of the perpendicular from P(3, 5, 7) onto the plane. Therefore, vector PQ is parallel to the normal to the plane. So 

(x₁, y₁, z₁) lies in the plane. This implies 

Therefore, Q = (x₁, y₁, z₁) = (−3, 2, 4). If P'(α,β,γ) is the image of P(3, 5, 7), then Q is the midpoint of vector PP' which implies that

Hence, the image of P = P' = (α,β,γ) = (−9, −1, 1)